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Discontinuous Galerkin method
On-line teaching, academic year 2020/21
Lecture Notes
LectureNotes_DGM.pdf
https://su.mff.cuni.cz/ - Records of the lectures, "studentske uloziste", CAS login required,
directory
/home/dolejsi/DiscontinuousGalerkinMethod
Week 1, March 2, 2021
- 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, March 9, 2021
No lecture
Week 3, March 16, 2021
- abstract error analysis
- basic notation
Week 4, March 23, 2021
- broken Sobolev spaces,
- discretization of the Laplace problem by DGM
- formulation of DG solution
Week 5, March 30, 2021
- formulation of DGM, notes on the realization of boundary conditions
- several tools known from the finite element method
- multiplicative trace inequality
Week 6, April 6, 2021
- inverse inequality
- approximation properties
- boundedness of the bilinear form
Week 7, April 13, 2021
- boundedness of the bilinear form in DG-norm
- coercivity
- existence of the solution
Week 8, April 20, 2021
- abstract error estimate in the DG-norm
- error estimate in terms of h
- error estimate in terms in the L^2-norm
Week 9, April 27, 2021
- 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
Solution should be send by e-mail no later than May 11, 2020
- 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
- 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!)
- DGM for the nonlinear convection-diffusion equation: Sections 2.1 – 2.2, in the Lecture notes.
Week 10, May 4, 2021
- DGM for the nonlinear convection-diffusion equation: Sections 2.2 – 2.3, in the Lecture notes.
Week 11, May 11, 2021
- DGM for the nonlinear convection-diffusion equation: Sections 2.3 – 2.4, 2.7 in the Lecture notes (skip Section 2.3.2)
- Discontinuous Galerkin method for a convection-diffusion equation: summary of results
pres4.pdf
- test_DGM2.pdf – test (quiz) #2
Solution should be send by e-mail no later than May 25, 2021
Week 12, May 18, 2021
- BDF DGM method: Chapter 3 in the Lecture notes, presentation: pres5.pdf
Week 13, May 25, 2021
- BDF DGM method: Chapter 3 in the Lecture notes, numerical experiments,
presentation: pres5.pdf
- STDGM method: Chapter 4 in the Lecture notes, presentation:
pres6.pdf
Week 14, June 1, 2021
- 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
Solution should be send by e-mail at least one day before the exam