├── .gitignore ├── 1-scientific-programming ├── .gitignore ├── Lecture-0-Scientific-Computing-with-Python.ipynb ├── Lecture-1-Introduction-to-Python-Programming.ipynb ├── Lecture-2-Numpy.ipynb ├── Lecture-3-Scipy.ipynb ├── Lecture-4-Matplotlib.ipynb ├── Lecture-5-Sympy.ipynb ├── Lecture-6A-Fortran-and-C.ipynb ├── Lecture-6B-HPC.ipynb ├── Lecture-7-Revision-Control-Software.ipynb ├── Makefile ├── README.md ├── Scientific-Computing-with-Python.pdf ├── Scientific-Computing-with-Python.tex ├── chapter.tplx ├── images │ ├── github-diff.png │ ├── github-project-page.png │ ├── gitk.png │ ├── ipython-notebook-screenshot.jpg │ ├── ipython-screenshot.jpg │ ├── optimizing-what-2.png │ ├── optimizing-what.png │ ├── python-screenshot.jpg │ ├── scientific-python-stack.png │ ├── scientific-python-stack.svg │ ├── spyder-screenshot.jpg │ ├── theory-experiment-computation.png │ └── theory-experiment-computation.svg ├── scripts │ ├── hello-world-in-swedish.py │ └── hello-world.py └── stockholm_td_adj.dat ├── 2-finite-difference-method ├── .gitignore ├── LICENSE ├── README.md ├── files │ └── CourseNotesMATH3018_6141.pdf ├── lessons │ ├── 00_getting_started │ │ ├── 00_01_Intro_to_the_command_line_osx.md │ │ ├── 00_01_Intro_to_the_command_line_redhat.md │ │ ├── 00_02_Installing_Jupyter.md │ │ ├── 00_03_Intro_to_Jupyter_notebook.md │ │ ├── 00_04_Intro_to_git.md │ │ └── images │ │ │ ├── 1.whoami.gif │ │ │ ├── 2.pwd.gif │ │ │ ├── 3.ls.gif │ │ │ ├── 4.cd.gif │ │ │ ├── 5.cdtabtab.gif │ │ │ ├── 6.bashrc.gif │ │ │ ├── addtopath.gif │ │ │ ├── anaconda.download.gif │ │ │ ├── condainstall.gif │ │ │ ├── mathjax.gif │ │ │ ├── movingcells.gif │ │ │ ├── newnotebook.gif │ │ │ ├── overwrite.gif │ │ │ ├── rendermarkdown.gif │ │ │ └── runandprint.gif │ ├── 01_phugoid │ │ ├── 01_01_Phugoid_Theory.ipynb │ │ ├── 01_02_Phugoid_Oscillation.ipynb │ │ ├── 01_03_PhugoidFullModel.ipynb │ │ ├── 01_04_Second_Order_Methods.ipynb │ │ ├── README.md │ │ ├── Rocket_Assignment.ipynb │ │ ├── figures │ │ │ ├── burn_rate.png │ │ │ ├── glider_forces-lesson3.png │ │ │ ├── glider_forces.png │ │ │ ├── glider_forces_fbd.svg │ │ │ ├── glider_forces_nodrag.png │ │ │ ├── glider_forces_nodrag.svg │ │ │ ├── oscillatory_trajectory.png │ │ │ ├── rocket_CV.png │ │ │ └── vonKarman-phugoids.png │ │ └── phugoid.py │ ├── 02_spacetime │ │ ├── 02_01_1DConvection.ipynb │ │ ├── 02_02_CFLCondition.ipynb │ │ ├── 02_03_1DDiffusion.ipynb │ │ ├── 02_04_1DBurgers.ipynb │ │ ├── README.md │ │ └── figures │ │ │ ├── CFLcondition.png │ │ │ ├── FDapproxiamtions.png │ │ │ ├── FTBS_stencil.png │ │ │ ├── characteristics.png │ │ │ ├── squarewave.png │ │ │ ├── stencil-1.png │ │ │ ├── stencil-2.png │ │ │ ├── stencil-3.png │ │ │ ├── stencil-4.png │ │ │ ├── vectorizedstencil.png │ │ │ └── vectorizedstencil.svg │ ├── 03_wave │ │ ├── 03_01_conservationLaw.ipynb │ │ ├── 03_02_convectionSchemes.ipynb │ │ ├── 03_03_aBetterModel.ipynb │ │ ├── 03_04_MUSCL.ipynb │ │ ├── 03_05_Sods_Shock_Tube.ipynb │ │ ├── README.md │ │ ├── figures │ │ │ ├── 1Dcontrolvolume.png │ │ │ ├── 1Dfluxbalance.png │ │ │ ├── FD-stencil_FTCS.png │ │ │ ├── FD-stencil_LF.png │ │ │ ├── FTBS_stencil.png │ │ │ ├── Riemann-shocktube.png │ │ │ ├── calc_sigma.svg │ │ │ ├── cell_boundaries.svg │ │ │ ├── finite_volume.png │ │ │ ├── finite_volume.svg │ │ │ ├── linear_extrapolation.png │ │ │ ├── linear_extrapolation.svg │ │ │ ├── linear_reconstruction.png │ │ │ ├── linear_reconstruction.svg │ │ │ ├── many_Rieman_problems.png │ │ │ ├── massconservation-CV.png │ │ │ ├── pipe1.png │ │ │ ├── pipe1.svg │ │ │ ├── richtmyer.png │ │ │ ├── shock_tube_.01.png │ │ │ ├── shocktube.png │ │ │ ├── squarewave.png │ │ │ ├── velocity_and_flux.png │ │ │ └── velocityvsdensity.png │ │ └── traffic.py │ ├── 04_spreadout │ │ ├── 04_00_Python_Function_Quirks.ipynb │ │ ├── 04_01_Heat_Equation_1D_Explicit.ipynb │ │ ├── 04_02_Heat_Equation_1D_Implicit.ipynb │ │ ├── 04_03_Heat_Equation_2D_Explicit.ipynb │ │ ├── 04_04_Heat_Equation_2D_Implicit.ipynb │ │ ├── 04_05_Crank-Nicolson.ipynb │ │ ├── 04_06_Reaction_Diffusion.ipynb │ │ ├── README.md │ │ ├── data │ │ │ └── uvinitial.npz │ │ └── figures │ │ │ ├── 2D_discretization.png │ │ │ ├── 2d_stencil.svg │ │ │ ├── 2dchip.svg │ │ │ ├── 2dgrid.svg │ │ │ ├── 2dgrid_indices.svg │ │ │ ├── A_1.svg │ │ │ ├── A_2.svg │ │ │ ├── A_3.svg │ │ │ ├── btcs_stencil.png │ │ │ ├── celldivision.gif │ │ │ ├── explicitFTCS-BCeffect.png │ │ │ ├── fingerprint.gif │ │ │ ├── graphite-rod.png │ │ │ ├── implicit-matrix-blocks.png │ │ │ ├── implicit_formula.png │ │ │ ├── implicit_formula.svg │ │ │ ├── implicit_matrix.svg │ │ │ ├── matrix-blocks-on-grid.png │ │ │ ├── rowcolumn.svg │ │ │ ├── stencil-cranknicolson.png │ │ │ ├── stencil-implicitcentral.png │ │ │ └── stencil-weights.png │ └── 05_relax │ │ ├── 05_01_2D.Laplace.Equation.ipynb │ │ ├── 05_02_2D.Poisson.Equation.ipynb │ │ ├── 05_03_Iterate.This.ipynb │ │ ├── 05_04_Conjugate.Gradient.ipynb │ │ ├── 05_05_Stokes.Flow.ipynb │ │ ├── README.md │ │ ├── data │ │ └── relaxation_schedules.npz │ │ ├── figures │ │ ├── drivencavity.svg │ │ ├── jumps.png │ │ ├── laplace.svg │ │ ├── solvepath.svg │ │ └── stokes_contour.svg │ │ ├── helper.py │ │ └── multigrid_helper.py ├── nm_python_env.yaml └── styles │ └── numericalmoocstyle.css ├── 3-finite-element-method ├── .gitignore ├── 0- preface.ipynb ├── 1- overview.ipynb ├── 2- approx-exercises.ipynb ├── 2- approx.ipynb ├── 3- approx-fe-exercises.ipynb ├── 3- approx-fe.ipynb ├── 3-FF_func_approx.edp ├── 4- varform-exercises.ipynb ├── 4- varform.ipynb ├── 5- varform-fe-exercises.ipynb ├── 5- varform-fe.ipynb ├── 5-FF_poisson.edp ├── 6-FF_time_diffusion.edp ├── 6-femtime-exercises.ipynb ├── 6-femtime.ipynb ├── 7- femsys.ipynb ├── 7-FF_stokes_cavity.edp ├── 8- nonlin.ipynb ├── 8-FF_newton.edp ├── 8-FF_picard.edp ├── 8-FF_picard_relaxation.edp ├── 9- cg.ipynb ├── 9-FF_preconditioning_hpc.edp ├── LICENSE.md ├── README.md ├── exer │ ├── Fourier_ls.py │ ├── Pd_approx_error.py │ ├── approx2D_ls_orth.py │ ├── approx3D.py │ ├── cable_1P2.py │ ├── cable_discont_load.py │ ├── cable_sin.py │ ├── cable_xn.py │ ├── exp_powers.py │ ├── fe_Heaviside_P1P2.py │ ├── fe_numberings1.py │ ├── fe_numberings2.py │ ├── fe_sin_P1.py │ ├── fe_sparsity_pattern.py │ ├── fe_tanh_P1P2.py │ ├── fe_tanh_P3P4.py │ ├── fu_fem_int.py │ ├── logistic_p.py │ ├── parabola_sin.py │ ├── product_arith_mean_sympy.py │ ├── run_all.sh │ ├── sin_powers.py │ ├── tanh_Lagrange.py │ ├── tanh_Lagrange_regression.py │ ├── tanh_sines.py │ ├── tanh_sines_approx_altsol.py │ ├── tanh_sines_boundary_term.py │ ├── u_xx_f_sympy_class.py │ └── u_xx_xm_P1to4.py ├── fig │ ├── AeA_vs_dt.png │ ├── AeA_vs_k.png │ ├── Bell_computations_loglog.pdf │ ├── Bell_computations_loglog.png │ ├── Bell_convergence_loglog.pdf │ ├── Bell_convergence_loglog.png │ ├── Bell_convergence_semilog.pdf │ ├── Bell_convergence_semilog.png │ ├── Bell_convergence_semilogy.png │ ├── Bernstein16.png │ ├── Bernstein8.png │ ├── BernsteinVSLagrange.png │ ├── Bernstein_basis8.png │ ├── Bernstein_convdiff_16.png │ ├── Bernstein_convdiff_8.png │ ├── ElmB4n2D_map.fig │ ├── ElmB4n2D_map.pdf │ ├── ElmB8n2D_map.fig │ ├── ElmB8n2D_map.pdf │ ├── ElmB9n2D_map.fig │ ├── ElmB9n2D_map.pdf │ ├── ElmT3n2D_map.fig │ ├── ElmT3n2D_map.pdf │ ├── ElmT3n2D_map.png │ ├── ElmT6n2D_map.fig │ ├── ElmT6n2D_map.pdf │ ├── ElmT6n2D_map.png │ ├── Fourier_Heaviside.pdf │ ├── Fourier_Heaviside.png │ ├── Lagrange_basis8.png │ ├── Lagrange_basis_12.pdf │ ├── Lagrange_basis_12.png │ ├── Lagrange_basis_15.pdf │ ├── Lagrange_basis_15.png │ ├── Lagrange_basis_8.pdf │ ├── Lagrange_basis_8.png │ ├── Lagrange_basis_Cheb_12.pdf │ ├── Lagrange_basis_Cheb_12.png │ ├── Lagrange_basis_Cheb_15.pdf │ ├── Lagrange_basis_Cheb_6.pdf │ ├── Lagrange_basis_Cheb_8.pdf │ ├── Lagrange_basis_unif_Cheb_12.pdf │ ├── Lagrange_basis_unif_Cheb_12.png │ ├── Lagrange_interp_abs_12.pdf │ ├── Lagrange_interp_abs_12.pdf.pdf │ ├── Lagrange_interp_abs_12.png │ ├── Lagrange_interp_abs_15.pdf │ ├── Lagrange_interp_abs_15.pdf.pdf │ ├── Lagrange_interp_abs_15.png │ ├── Lagrange_interp_abs_8.pdf │ ├── Lagrange_interp_abs_8.pdf.pdf │ ├── Lagrange_interp_abs_8.png │ ├── Lagrange_interp_abs_8_15.pdf │ ├── Lagrange_interp_abs_8_15.png │ ├── Lagrange_interp_abs_Cheb_12.pdf │ ├── Lagrange_interp_abs_Cheb_12.png │ ├── Lagrange_interp_abs_Cheb_15.pdf │ ├── Lagrange_interp_abs_Cheb_15.png │ ├── Lagrange_interp_abs_Cheb_5.pdf │ ├── Lagrange_interp_abs_Cheb_8.pdf │ ├── Lagrange_interp_abs_Cheb_8.png │ ├── Lagrange_interp_abs_Cheb_8_15.pdf │ ├── Lagrange_interp_abs_Cheb_8_15.png │ ├── Lagrange_interp_abs_Cheb_9.pdf │ ├── Lagrange_interp_p2_3.pdf │ ├── Lagrange_interp_p2_3.png │ ├── Lagrange_interp_sin_4.pdf │ ├── Lagrange_interp_sin_4.png │ ├── Lagrange_interp_sin_6.pdf │ ├── Lagrange_interp_tanh_10.pdf │ ├── Lagrange_interp_tanh_12.pdf │ ├── Lagrange_interp_tanh_4.pdf │ ├── Lagrange_interp_tanh_7.pdf │ ├── Lagrange_interp_tanh_Cheb_10.pdf │ ├── Lagrange_interp_tanh_Cheb_12.pdf │ ├── Lagrange_interp_tanh_Cheb_4.pdf │ ├── Lagrange_interp_tanh_Cheb_7.pdf │ ├── Lagrange_ls_abs_12.pdf │ ├── Lagrange_ls_abs_12.png │ ├── Lagrange_ls_abs_8.pdf │ ├── Lagrange_ls_interp_sin_4.pdf │ ├── Lagrange_ls_interp_sin_4.png │ ├── Lagrange_ls_sin_4.pdf │ ├── Lagrange_ls_sin_4.png │ ├── Lagrange_ls_sin_6.pdf │ ├── P1-1d2d3d.pdf │ ├── P1-1d2d3d.png │ ├── P1-6_2d.pdf │ ├── P1-6_2d.png │ ├── P1_2d.pdf │ ├── P1_2d.png │ ├── P2-1d2d3d.pdf │ ├── P2-1d2d3d.png │ ├── P2_2d.pdf │ ├── P2_2d.png │ ├── approx2D_bilinear.pdf │ ├── approx2D_bilinear.png │ ├── approx2D_ls_orth_sine_c.pdf │ ├── approx2D_ls_orth_sine_c.png │ ├── approx_fenics_f1.pdf │ ├── approx_fenics_f1.png │ ├── approx_fenics_f1_by_P0.pdf │ ├── approx_fenics_f1_by_P0.png │ ├── approx_fenics_f1_by_P1.pdf │ ├── approx_fenics_f1_by_P1.png │ ├── approx_fenics_f1_by_P2.pdf │ ├── approx_fenics_f1_by_P2.png │ ├── borehole1.pdf │ ├── borehole1.png │ ├── borehole_mesh1.pdf │ ├── borehole_mesh1.png │ ├── cable_discont_load_P1.pdf │ ├── cable_discont_load_P1.png │ ├── cable_discont_load_sines.pdf │ ├── cable_discont_load_sines.png │ ├── cable_discont_load_u_exact.pdf │ ├── cable_discont_load_u_exact.png │ ├── cable_sin_c.pdf │ ├── cable_sin_c.png │ ├── cable_sin_d.pdf │ ├── cable_sin_d.png │ ├── conv-diff-analytical.png │ ├── conv-diff-osc.png │ ├── conv-diff-stab.png │ ├── conv-diff.png │ ├── cooling_T.png │ ├── cooling_w.png │ ├── darcy_a1D.pdf │ ├── darcy_a1D.png │ ├── darcy_a1D_mx.pdf │ ├── darcy_a1D_mx.png │ ├── darcy_adx1D.pdf │ ├── darcy_adx1D.png │ ├── darcy_adx1D_mx.pdf │ ├── darcy_adx1D_mx.png │ ├── delta_func_weight.pdf │ ├── delta_func_weight.png │ ├── delta_func_weight.py │ ├── demo2D_2x2c.pdf │ ├── demo2D_2x2c.png │ ├── demo2D_2x2r.pdf │ ├── demo2D_2x2r.png │ ├── demo2D_2x3r.pdf │ ├── demo2D_2x3r.png │ ├── demo2D_3x3r.pdf │ ├── demo2D_3x3r.png │ ├── demo2D_4x3r.pdf │ ├── demo2D_4x3r.png │ ├── demo2D_4x4r.pdf │ ├── demo2D_4x4r.png │ ├── demo2D_4x5r.pdf │ ├── demo2D_4x5r.png │ ├── demo2D_basisfunc.pdf │ ├── demo2D_basisfunc.png │ ├── diffu_A_factors3_BE.pdf │ ├── diffu_A_factors3_BE.png │ ├── diffu_A_factors3_FE.pdf │ ├── diffu_A_factors3_FE.png │ ├── diffu_A_factors_BE.pdf │ ├── diffu_A_factors_BE.png │ ├── diffu_A_factors_CN.pdf │ ├── diffu_A_factors_CN.png │ ├── diffu_A_factors_coarse_BE.pdf │ ├── diffu_A_factors_coarse_BE.png │ ├── diffu_A_factors_coarse_CN.pdf │ ├── diffu_A_factors_coarse_CN.png │ ├── diffu_A_factors_coarse_FE.pdf │ ├── diffu_A_factors_coarse_FE.png │ ├── diffu_A_factors_fine_BE.pdf │ ├── diffu_A_factors_fine_BE.png │ ├── diffu_A_factors_fine_CN.pdf │ ├── diffu_A_factors_fine_CN.png │ ├── diffu_A_factors_fine_FE.pdf │ ├── diffu_A_factors_fine_FE.png │ ├── dolfin_flow.gif │ ├── dolfin_flow.pdf │ ├── dolfin_mesh.png │ ├── error_rates_global.png │ ├── exp_powers_N2.pdf │ ├── exp_powers_N2.png │ ├── fe_Heaviside_P1.pdf │ ├── fe_Heaviside_P1.png │ ├── fe_Heaviside_P2.pdf │ ├── fe_Heaviside_P2.png │ ├── fe_Heaviside_P3.pdf │ ├── fe_Heaviside_P3.png │ ├── fe_Heaviside_P4.pdf │ ├── fe_Heaviside_P4.png │ ├── fe_mesh1D_P1.pdf │ ├── fe_mesh1D_P1.png │ ├── fe_mesh1D_P2.pdf │ ├── fe_mesh1D_P2.png │ ├── fe_mesh1D_P2_4e.pdf │ ├── fe_mesh1D_P2_4e.png │ ├── fe_mesh1D_d4_stretched.pdf │ ├── fe_mesh1D_d4_stretched.png │ ├── fe_mesh1D_dphi_2_3.pdf │ ├── fe_mesh1D_dphi_2_3.png │ ├── fe_mesh1D_phi_2_3.pdf │ ├── fe_mesh1D_phi_2_3.png │ ├── fe_mesh1D_phi_i_f.pdf │ ├── fe_mesh1D_phi_i_f.png │ ├── fe_mesh1D_phi_i_im1.pdf │ ├── fe_mesh1D_phi_i_im1.png │ ├── fe_mesh1D_random_numbering.pdf │ ├── fe_mesh1D_random_numbering.png │ ├── fe_p0_x2_2e_4e.png │ ├── fe_p0_x2_4e.pdf │ ├── fe_p0_x2_4e.png │ ├── fe_p0_x2_4e_8e.pdf │ ├── fe_p0_x2_4e_8e.png │ ├── fe_p0_x2_8e.pdf │ ├── fe_p0_x2_8e.png │ ├── fe_p12_x9_248e.pdf │ ├── fe_p12_x9_248e.png │ ├── fe_p1_p2_x9_248e.pdf │ ├── fe_p1_p2_x9_248e.png │ ├── fe_p1_sin2_4e.pdf │ ├── fe_p1_sin2_4e.png │ ├── fe_p1_sin_4e.pdf │ ├── fe_p1_sin_4e.png │ ├── fe_p1_tanh.pdf │ ├── fe_p1_tanh.png │ ├── fe_p1_tanh_20e.pdf │ ├── fe_p1_tanh_4e.pdf │ ├── fe_p1_tanh_8e.pdf │ ├── fe_p1_x2_2e.pdf │ ├── fe_p1_x2_2e.png │ ├── fe_p1_x2_2e_4e.pdf │ ├── fe_p1_x2_2e_4e.png │ ├── fe_p1_x2_4e.pdf │ ├── fe_p1_x2_4e.png │ ├── fe_p1_x2_4e_8e.pdf │ ├── fe_p1_x2_4e_8e.png │ ├── fe_p1_x2_8e.pdf │ ├── fe_p1_x2_8e.png │ ├── fe_p1_x9_4e.pdf │ ├── fe_p1_x9_4e.png │ ├── fe_p1_x9_8e.pdf │ ├── fe_p1_x9_8e.png │ ├── fe_p1_x_4e.pdf │ ├── fe_p1_x_4e.png │ ├── fe_p2_sin2_2e.pdf │ ├── fe_p2_sin2_2e.png │ ├── fe_p2_sin2_4e.pdf │ ├── fe_p2_sin2_4e.png │ ├── fe_p2_sin_2e.pdf │ ├── fe_p2_sin_2e.png │ ├── fe_p2_sin_4e.pdf │ ├── fe_p2_sin_4e.png │ ├── fe_p2_tanh.pdf │ ├── fe_p2_tanh.png │ ├── fe_p2_tanh_4e.pdf │ ├── fe_p2_tanh_8e.pdf │ ├── fe_p2_x2_1e.pdf │ ├── fe_p2_x2_1e.png │ ├── fe_p2_x2_4e.pdf │ ├── fe_p2_x2_4e.png │ ├── fe_p2_x9_2e.pdf │ ├── fe_p2_x9_2e.png │ ├── fe_p2_x9_4e.pdf │ ├── fe_p2_x9_4e.png │ ├── fe_p3_tanh.pdf │ ├── fe_p3_tanh.png │ ├── fe_p4_tanh.pdf │ ├── fe_p4_tanh.png │ ├── fe_p4_tanh_4e.pdf │ ├── fe_p4_tanh_8e.pdf │ ├── fe_tanh_interpol_P3.pdf │ ├── fe_tanh_interpol_P3.png │ ├── fe_tanh_interpol_P4.pdf │ ├── fe_tanh_interpol_P4.png │ ├── fenics-book │ │ ├── elements │ │ │ ├── P1-1d2d3d.pdf │ │ │ ├── P1-1d2d3d.png │ │ │ ├── P1-6_2d.pdf │ │ │ ├── P1-6_2d.png │ │ │ ├── P1_2d.pdf │ │ │ ├── P1_2d.png │ │ │ ├── P2-1d2d3d.pdf │ │ │ ├── P2-1d2d3d.png │ │ │ ├── P2_2d.pdf │ │ │ ├── P2_2d.png │ │ │ ├── P3_2d.pdf │ │ │ └── P3_2d.png │ │ ├── eps │ │ │ ├── ARG5.eps │ │ │ ├── BDM1.eps │ │ │ ├── BDM2.eps │ │ │ ├── BDM3.eps │ │ │ ├── CR1.eps │ │ │ ├── HER3.eps │ │ │ ├── MOR2.eps │ │ │ ├── NED1.eps │ │ │ ├── NED2.eps │ │ │ ├── NED3.eps │ │ │ ├── P1-1d2d3d.eps │ │ │ ├── P1-6.eps │ │ │ ├── P1.eps │ │ │ ├── P2-1d2d3d.eps │ │ │ ├── P2.eps │ │ │ ├── P3.eps │ │ │ ├── PEERS.eps │ │ │ ├── RT0.eps │ │ │ ├── RT1.eps │ │ │ ├── RT2.eps │ │ │ └── notation.eps │ │ └── svg │ │ │ ├── P1-1d2d3d.svg │ │ │ ├── P1-6_2d.svg │ │ │ ├── P1_2d.svg │ │ │ ├── P2-1d2d3d.svg │ │ │ ├── P2_2d.svg │ │ │ ├── P3_2d.svg │ │ │ └── README │ ├── fenics_2D_plot_approx.pdf │ ├── fenics_2D_plot_approx.png │ ├── fenics_conv_diff.pdf │ ├── fenics_conv_diff.png │ ├── fenics_conv_diff_stab.pdf │ ├── fenics_conv_diff_stab.png │ ├── fenics_plot_along_line.pdf │ ├── fenics_plot_along_line.png │ ├── finite_element_mesh.pdf │ ├── finite_element_mesh.png │ ├── grid-demo-P1.pdf │ ├── grid-demo-P1.png │ ├── grid-demo-Q1.pdf │ ├── grid-demo-Q1.png │ ├── ill_conditioning.pdf │ ├── ill_conditioning.png │ ├── illegal-node.fig │ ├── illegal-node.pdf │ ├── illegal-node.png │ ├── logistic_N100_eps-04_iter.pdf │ ├── logistic_N100_eps-04_iter.png │ ├── logistic_N100_eps-04_u.pdf │ ├── logistic_N100_eps-04_u.png │ ├── logistic_N10_eps-01_iter.pdf │ ├── logistic_N10_eps-01_iter.png │ ├── logistic_N10_eps-01_u.pdf │ ├── logistic_N10_eps-01_u.png │ ├── logistic_N10_eps-03_iter.pdf │ ├── logistic_N10_eps-03_iter.png │ ├── logistic_N10_eps-03_u.pdf │ ├── logistic_N10_eps-03_u.png │ ├── logistic_N20_eps-03_iter.pdf │ ├── logistic_N20_eps-03_iter.png │ ├── logistic_N20_eps-03_u.pdf │ ├── logistic_N20_eps-03_u.png │ ├── logistic_iter.pdf │ ├── logistic_iter.png │ ├── logistic_u.pdf │ ├── logistic_u.png │ ├── matrix-assembly.fig │ ├── matrix-assembly.pdf │ ├── matrix-assembly.png │ ├── mesh2D_quarter_circle.pdf │ ├── mesh2D_quarter_circle.png │ ├── mesh2D_rect_P1.pdf │ ├── mesh2D_rect_P1.png │ ├── mesh2D_rect_Q1.pdf │ ├── mesh2D_rect_Q1.png │ ├── mesh2D_rect_crossed.pdf │ ├── mesh2D_rect_crossed.png │ ├── mesh2D_rect_left.pdf │ ├── mesh2D_rect_left.png │ ├── mesh2D_rect_left_right.pdf │ ├── mesh2D_rect_left_right.png │ ├── neumann_fixpoint.png │ ├── neumann_fixpoint_exact.png │ ├── nitsche1D.png │ ├── nitsche1D_zoom.png │ ├── noisy_parabola_by_linear_regression.pdf │ ├── noisy_parabola_by_linear_regression.png │ ├── noisy_parabola_by_quadratic_regression.pdf │ ├── noisy_parabola_by_quadratic_regression.png │ ├── parabola_by_regression.pdf │ ├── parabola_by_regression.png │ ├── parabola_inter.pdf │ ├── parabola_inter.png │ ├── parabola_interp12_linear.pdf │ ├── parabola_interp1_linear.pdf │ ├── parabola_interp1_linear.png │ ├── parabola_interp2_linear.pdf │ ├── parabola_interp2_linear.png │ ├── parabola_interp3_quadratic.pdf │ ├── parabola_interp3_quadratic.png │ ├── parabola_ls_linear.pdf │ ├── parabola_ls_linear.png │ ├── parabola_ls_sines12.pdf │ ├── parabola_ls_sines12.png │ ├── parabola_ls_sines12_wfterm.pdf │ ├── parabola_ls_sines12_wfterm.png │ ├── parabola_ls_sines4.pdf │ ├── parabola_ls_sines4.png │ ├── parabola_ls_sines4_12.pdf │ ├── parabola_ls_sines4_12.png │ ├── parabola_ls_sines4_12_wfterm.pdf │ ├── parabola_ls_sines4_12_wfterm.png │ ├── parabola_ls_sines4_wfterm.pdf │ ├── parabola_ls_sines4_wfterm.png │ ├── parabola_sin_a.pdf │ ├── parabola_sin_a.png │ ├── parabola_sin_b.pdf │ ├── parabola_sin_b.png │ ├── phi │ │ ├── mpl_fe_basis_p1_4e.pdf │ │ ├── mpl_fe_basis_p1_4e.png │ │ ├── mpl_fe_basis_p1_4e_lab.pdf │ │ ├── mpl_fe_basis_p1_4e_lab.png │ │ ├── mpl_fe_basis_p1_5e.pdf │ │ ├── mpl_fe_basis_p1_5e.png │ │ ├── mpl_fe_basis_p1_5e_lab.pdf │ │ ├── mpl_fe_basis_p1_5e_lab.png │ │ ├── mpl_fe_basis_p2_4e.pdf │ │ ├── mpl_fe_basis_p2_4e.pdf~HEAD │ │ ├── mpl_fe_basis_p2_4e.png │ │ ├── mpl_fe_basis_p2_4e_lab.pdf │ │ ├── mpl_fe_basis_p2_4e_lab.pdf~HEAD │ │ ├── mpl_fe_basis_p2_4e_lab.png │ │ ├── mpl_fe_basis_p3_4e.pdf │ │ ├── mpl_fe_basis_p3_4e.png │ │ ├── mpl_fe_basis_p3_4e_lab.pdf │ │ ├── mpl_fe_basis_p3_4e_lab.png │ │ ├── mpl_fe_basis_p3_5e.pdf │ │ ├── mpl_fe_basis_p3_5e.png │ │ ├── mpl_fe_basis_p3_5e_lab.pdf │ │ ├── mpl_fe_basis_p3_5e_lab.png │ │ ├── mpl_fe_dbasis_p1_4e.pdf │ │ ├── mpl_fe_dbasis_p1_4e.png │ │ ├── mpl_fe_dbasis_p1_4e_lab.pdf │ │ ├── mpl_fe_dbasis_p1_4e_lab.png │ │ ├── mpl_fe_dbasis_p1_5e.pdf │ │ ├── mpl_fe_dbasis_p1_5e.png │ │ ├── mpl_fe_dbasis_p1_5e_lab.pdf │ │ ├── mpl_fe_dbasis_p1_5e_lab.png │ │ ├── mpl_fe_dbasis_p2_4e.pdf │ │ ├── mpl_fe_dbasis_p2_4e.png │ │ ├── mpl_fe_dbasis_p2_4e_lab.pdf │ │ ├── mpl_fe_dbasis_p2_4e_lab.png │ │ └── old │ │ │ ├── gpl_fe_basis_p1_4e.pdf │ │ │ ├── gpl_fe_basis_p1_4e.png │ │ │ ├── gpl_fe_basis_p1_4e_lab.pdf │ │ │ ├── gpl_fe_basis_p1_5e.pdf │ │ │ ├── gpl_fe_basis_p1_5e.png │ │ │ ├── gpl_fe_basis_p1_5e_lab.pdf │ │ │ ├── gpl_fe_basis_p2_4e.pdf │ │ │ ├── gpl_fe_basis_p2_4e.png │ │ │ ├── gpl_fe_basis_p2_4e_lab.pdf │ │ │ ├── gpl_fe_basis_p3_4e.pdf │ │ │ ├── gpl_fe_basis_p3_4e.png │ │ │ ├── gpl_fe_basis_p3_4e_lab.pdf │ │ │ ├── gpl_fe_basis_p3_5e.pdf │ │ │ ├── gpl_fe_basis_p3_5e.png │ │ │ ├── gpl_fe_basis_p3_5e_lab.pdf │ │ │ ├── gpl_fe_dbasis_p1_4e_lab.pdf │ │ │ ├── gpl_fe_dbasis_p1_5e_lab.pdf │ │ │ └── gpl_fe_dbasis_p2_4e_lab.pdf │ ├── pyramid.fig │ ├── pyramid.pdf │ ├── pyramid.png │ ├── sin_powers_N7_V1_Omega1.pdf │ ├── sin_powers_N7_V1_Omega1.png │ ├── sin_powers_N7_V1_Omega2.pdf │ ├── sin_powers_N7_V1_Omega2.png │ ├── sin_powers_N7_V2_Omega1.pdf │ ├── sin_powers_N7_V2_Omega1.png │ ├── sin_powers_N7_V2_Omega2.pdf │ ├── sin_powers_N7_V2_Omega2.png │ ├── sin_taylor7.pdf │ ├── sin_taylor7.png │ ├── sinix_int.pdf │ ├── sinix_int.png │ ├── sparsity_pattern_1DP3_30.pdf │ ├── sparsity_pattern_1DP3_30.png │ ├── sparsity_pattern_1DP3_30rand.pdf │ ├── sparsity_pattern_1DP3_30rand.png │ ├── sparsity_pattern_1DP3_30unif.pdf │ ├── sparsity_pattern_1DP3_30unif.png │ ├── sparsity_pattern_1D_30.pdf │ ├── sparsity_pattern_1D_30.png │ ├── sparsity_pattern_1D_30rand.pdf │ ├── sparsity_pattern_1D_30rand.png │ ├── sparsity_pattern_1D_30unif.pdf │ ├── sparsity_pattern_1D_30unif.png │ ├── tanh_Lagrange_Chebyshev_s20.pdf │ ├── tanh_Lagrange_Chebyshev_s20.png │ ├── tanh_Lagrange_Chebyshev_s5.pdf │ ├── tanh_Lagrange_Chebyshev_s5.png │ ├── tanh_Lagrange_regr_Chebyshev_s20.pdf │ ├── tanh_Lagrange_regr_Chebyshev_s20.png │ ├── tanh_Lagrange_regr_Chebyshev_s5.pdf │ ├── tanh_Lagrange_regr_Chebyshev_s5.png │ ├── tanh_Lagrange_regr_uniform_s20.pdf │ ├── tanh_Lagrange_regr_uniform_s20.png │ ├── tanh_Lagrange_regr_uniform_s5.pdf │ ├── tanh_Lagrange_regr_uniform_s5.png │ ├── tanh_Lagrange_uniform_s20.pdf │ ├── tanh_Lagrange_uniform_s20.png │ ├── tanh_Lagrange_uniform_s5.pdf │ ├── tanh_Lagrange_uniform_s5.png │ ├── tanh_fe_interpol_P3.pdf │ ├── tanh_fe_interpol_P3.png │ ├── tanh_fe_interpol_P4.pdf │ ├── tanh_fe_interpol_P4.pdf.pdf │ ├── tanh_fe_interpol_P4.png │ ├── tanh_sines.pdf │ ├── tanh_sines.png │ ├── tanh_sines_boundary_term_a.pdf │ ├── tanh_sines_boundary_term_a.png │ ├── tanh_sines_boundary_term_b.pdf │ ├── tanh_sines_boundary_term_b.png │ ├── tanh_sines_boundary_term_c.pdf │ ├── tanh_sines_boundary_term_c.png │ ├── u_example_P1.pdf │ ├── u_example_P1.png │ ├── u_example_fe2.pdf │ ├── u_example_fe2.png │ ├── u_example_sin.pdf │ ├── u_example_sin.png │ ├── u_xx_xm0_P1to4.pdf │ ├── u_xx_xm0_P1to4.png │ ├── u_xx_xm1_P1to4.pdf │ ├── u_xx_xm1_P1to4.png │ ├── u_xx_xm2_P1to4.pdf │ ├── u_xx_xm2_P1to4.png │ ├── u_xx_xm3_P1to4.pdf │ ├── u_xx_xm3_P1to4.png │ ├── u_xx_xm4_P1to4.pdf │ ├── u_xx_xm4_P1to4.png │ ├── uxx_x2.pdf │ ├── uxx_x2.png │ ├── vecapprox_plane.gnu │ ├── vecapprox_plane.pdf │ └── vecapprox_plane.png ├── mov │ ├── fe_assembly.html │ ├── fe_assembly.sh │ ├── fe_assembly_irregular.pdf │ ├── fe_assembly_irregular.png │ ├── fe_assembly_irregular │ │ ├── fe_assembly_irregular.pdf │ │ ├── fe_assembly_irregular.png │ │ ├── fe_mesh.png │ │ ├── frame_0000.png │ │ ├── frame_0001.png │ │ ├── frame_0002.png │ │ ├── frame_0003.png │ │ ├── frame_0004.png │ │ ├── frame_0005.png │ │ ├── frame_0006.png │ │ ├── frame_0007.png │ │ ├── frame_0008.png │ │ ├── frame_0009.png │ │ ├── frame_0010.png │ │ ├── frame_0011.png │ │ ├── frame_0012.png │ │ ├── frame_0013.png │ │ ├── frame_0014.png │ │ ├── frame_0015.png │ │ ├── frame_0016.png │ │ ├── frame_0017.png │ │ ├── frame_0018.png │ │ ├── frame_0019.png │ │ ├── index.html │ │ └── movie.gif │ ├── fe_assembly_regular_2x2.pdf │ ├── fe_assembly_regular_2x2.png │ ├── fe_assembly_regular_2x2 │ │ ├── fe_assembly_regular_2x2.pdf │ │ ├── fe_assembly_regular_2x2.png │ │ ├── fe_mesh.png │ │ ├── frame_0000.png │ │ ├── frame_0001.png │ │ ├── frame_0002.png │ │ ├── frame_0003.png │ │ ├── frame_0004.png │ │ ├── frame_0005.png │ │ ├── frame_0006.png │ │ ├── frame_0007.png │ │ ├── frame_0008.png │ │ ├── frame_0009.png │ │ ├── frame_0010.png │ │ ├── frame_0011.png │ │ ├── frame_0012.png │ │ ├── frame_0013.png │ │ ├── frame_0014.png │ │ ├── frame_0015.png │ │ ├── index.html │ │ └── movie.gif │ ├── fe_assembly_regular_4x4.pdf │ ├── fe_assembly_regular_4x4.png │ ├── fe_assembly_regular_4x4 │ │ ├── fe_assembly_regular_4x4.pdf │ │ ├── fe_assembly_regular_4x4.png │ │ ├── fe_mesh.png │ │ ├── frame_0000.png │ │ ├── frame_0001.png │ │ ├── frame_0002.png │ │ ├── frame_0003.png │ │ ├── frame_0004.png │ │ ├── frame_0005.png │ │ ├── frame_0006.png │ │ ├── frame_0007.png │ │ ├── frame_0008.png │ │ ├── frame_0009.png │ │ ├── frame_0010.png │ │ ├── frame_0011.png │ │ ├── frame_0012.png │ │ ├── frame_0013.png │ │ ├── frame_0014.png │ │ ├── frame_0015.png │ │ ├── frame_0016.png │ │ ├── frame_0017.png │ │ ├── frame_0018.png │ │ ├── frame_0019.png │ │ ├── frame_0020.png │ │ ├── frame_0021.png │ │ ├── frame_0022.png │ │ ├── frame_0023.png │ │ ├── frame_0024.png │ │ ├── frame_0025.png │ │ ├── frame_0026.png │ │ ├── frame_0027.png │ │ ├── frame_0028.png │ │ ├── frame_0029.png │ │ ├── frame_0030.png │ │ ├── frame_0031.png │ │ ├── frame_0032.png │ │ ├── frame_0033.png │ │ ├── frame_0034.png │ │ ├── frame_0035.png │ │ ├── frame_0036.png │ │ ├── frame_0037.png │ │ ├── frame_0038.png │ │ ├── frame_0039.png │ │ ├── frame_0040.png │ │ ├── frame_0041.png │ │ ├── frame_0042.png │ │ ├── frame_0043.png │ │ ├── frame_0044.png │ │ ├── frame_0045.png │ │ ├── frame_0046.png │ │ ├── frame_0047.png │ │ ├── frame_0048.png │ │ ├── frame_0049.png │ │ ├── frame_0050.png │ │ ├── frame_0051.png │ │ ├── frame_0052.png │ │ ├── frame_0053.png │ │ ├── frame_0054.png │ │ ├── frame_0055.png │ │ ├── frame_0056.png │ │ ├── frame_0057.png │ │ ├── frame_0058.png │ │ ├── frame_0059.png │ │ ├── frame_0060.png │ │ ├── frame_0061.png │ │ ├── frame_0062.png │ │ ├── frame_0063.png │ │ ├── index.html │ │ └── movie.gif │ ├── index.html │ ├── tanh_sines.gif │ ├── tanh_sines_boundary_term_a.gif │ ├── tanh_sines_boundary_term_b.gif │ └── tanh_sines_boundary_term_c.gif ├── src │ ├── Bernstein_vs_Lagrange.output │ ├── Bernstein_vs_Lagrange.py │ ├── Bernstein_vs_Lagrange_plot.py │ ├── Lagrange.py │ ├── Lagrange_multiplier.py │ ├── Newton_demo.py │ ├── Newton_demo_session.sh │ ├── ODE_Picard_tricks.py │ ├── approx1D.py │ ├── approx2D.py │ ├── approx_fenics.py │ ├── approx_fenics_2Dcase.py │ ├── borehole_fenics.py │ ├── clean.sh │ ├── conv-diff-global.py │ ├── conv-diff-pg.py │ ├── conv-diff-stab.py │ ├── conv-diff.py │ ├── convergence_rate_fem.py │ ├── convergence_rate_global.output │ ├── convergence_rate_global.py │ ├── convergence_rate_local.py │ ├── darcy1D.py │ ├── darcy1D_mixed.py │ ├── diffop_lib.py │ ├── dispersion_relations.py │ ├── ex_approx1D.py │ ├── ex_approx1D.sh │ ├── ex_approx1D_session.py │ ├── ex_approx2D.py │ ├── ex_fe_approx1D.py │ ├── ex_fe_approx1D_session.py │ ├── ex_varform1D.py │ ├── fe1D.py │ ├── fe_approx1D.py │ ├── fe_approx1D_numint.py │ ├── fe_approx1D_v1.py │ ├── fe_approx2D.py │ ├── fe_fast_approx1D.py │ ├── integrate_Heaviside.py │ ├── logistic.py │ ├── logistic.sh │ ├── logistic_gen.py │ ├── mx_poisson.py │ ├── neumann_fixpoint.py │ ├── neumann_lagrangemultipler.py │ ├── nitsche.py │ ├── numint.py │ ├── pipecooling_fem.py │ ├── plot_fe_approx2D.py │ ├── plot_global_bell.py │ ├── plot_phi.py │ ├── plot_phi.sh │ ├── run_all.sh │ ├── sympy_bvp_exact.py │ ├── tanh_approx.py │ ├── u_xx_2_CD.py │ ├── u_xx_f_sympy.py │ ├── varform1D.py │ └── varform1D_session.py └── text_original │ ├── .2-approx.exerinfo │ ├── .3-varform.exerinfo │ ├── .4-femtime.exerinfo │ ├── .5-femsys.exerinfo │ ├── 0-preface.do.txt │ ├── 00-preface2.do.txt │ ├── 1-overview.do.txt │ ├── 2-approx.do.txt │ ├── 3-varform.do.txt │ ├── 4-femtime.do.txt │ ├── 5-femsys.do.txt │ ├── 6-nitsche.do.txt │ ├── 7-1-nonlin_pde1D.do.txt │ ├── 7-2-nonlin_pde_gen.do.txt │ ├── 7-nonlin_ode.do.txt │ ├── 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