Week 2, February 24, 2026

• 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
• abstract error analysis, Section 1.2

Week 3, March 3, 2026

• basic notation, Section 1.3
• broken Sobolev spaces, Section 1.3
• mesh assumptions, Section 1.3
• discretization of the Laplace problem by DGM, Section 1.4

Week 4, March 10, 2026

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

Week 5, March 17, 2026

• boundedness of the bilinear forms, Section 1.6

Week 6, March 24, 2026

• 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 31, 2026

• 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 7, 2026

• 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 14, 2026

• 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!)
• stabilizaton -- capturing of discontinuities, Section 6.5
• approximation of non-polygonal boundaries, Section 6.6