Week 1, February 14, 2023

• Motivation: numerical solution of partial differential equations, presentation Lecture_DGM1.pdf (full), Lecture_DGM1_brief.pdf (brief, suitable for printing)
• Propagation by a peak by connvection: conv.avi
• Propagation by a peak by diffusion: diff.avi
• Propagation by a peak by connvection-diffusion: conv+diff.avi
• Effect of diffusion for 1D linear convection-diffusion equation: exactCD.avi
• Comparison of FEM and FVM for 1D linear convection: FV-FE.avi

Week 2, February 21, 2023

• abstract error analysis, Section 1.2
• basic notation, Section 1.3
• broken Sobolev spaces, Section 1.3

Week 3, February 28, 2023

• discretization of the Laplace problem by DGM, Section 1.4
• formulation of DG solution, Section 1.4
• multiplicative trace inequality, Section 1.5

Week 4, March 7, 2023

• inverse inequality, Section 1.5
• approximation properties, Section 1.5
• boundedness of the bilinear forms, Section 1.6

Week 5, March 14, 2023

• boundedness of the bilinear forms, Section 1.6
• coercivity, Section 1.6

Week 6, March 21, 2023

• coercivity, Section 1.6
• existence of the solution, Section 1.6
• abstract error estimate in the DG-norm, Section 1.7
• error estimate in terms of h , Section 1.7

Week 7, March 28, 2023

• error estimate in terms in the L^2-norm
• numerical experiments, experimental order of convergence
• pres1.pdf   – summary of the main results of Chapter 1 from Lecture notes
• test_DGM1.pdf   – test (quiz) #1

Week 8, April 4, 2023

• finite volume method for the discretization of convective terms pres2.pdf (contains an internal animation working only in acroread)
  An additional external animation FV-FE.avi

Week 9, April 11, 2023

• Discontinuous Galerkin method for first order hyperbolic problems pres3.pdf, more detailed description is given in Chapter 6 in the Lecture notes (not necessary to study!)

Week 10, April 18, 2023

• DGM for the nonlinear convection-diffusion equation: Sections 2.2 – 2.3, in the Lecture notes.

Week 11, April 25, 2023

• DGM for the nonlinear convection-diffusion equation: Sections 2.3 – 2.4 in the Lecture notes (skip Section 2.3.2)

Week 12, May 2, 2023

• DGM for the nonlinear convection-diffusion equation: Sections 2.4, 2.5, 2.7 in the Lecture notes
• Discontinuous Galerkin method for a convection-diffusion equation: summary of results pres4.pdf
• test_DGM2.pdf   – test (quiz) #2

Week 13, May 9, 2023

• BDF DGM method: Chapter 3 in the Lecture notes, numerical experiments, presentation: pres5.pdf

Week 14, May 16, 2023

• STDGM method: Chapter 4 in the Lecture notes, presentation: pres6.pdf
• Adaptive computation by STDGM method, presentation: pres7.pdf (use acroread or okular for seeing the animation)
• test_DGM3.pdf   – test (quiz) #3