Numerical Methods For Stationary PDEs
Topics include: Maximum principle, finite difference method, upwinding, error analysis; Variational formulation of elliptic problems, inf-sup theory; The finite element method and its implementation; Piecewise polynomial interpolation theory in Sobolev spaces; A priori and a posteriori error analyses, adaptivity; Fast solvers; Variational crimes; Mixed finite element methods.
Topics
- Maximum principle
- finite difference method
- upwinding
- error analysis
- Variational formulation of elliptic problems
- inf-sup theory
- The finite element method and its implementation
- Piecewise polynomial interpolation theory in Sobolev spaces
- A priori and a posteriori error analyses
- adaptivity
- Fast solvers
- Variational crimes
- Mixed finite element methods
Topics explicitly listed in official catalogue description
Prerequisites & course information
Credit Only Granted for: AMSC 714 or AMSC 614. Formerly: AMSC614. Additional Information: This course is a complement to the graduate courses MATH 673 and MATH 674 in PDEs, AMSC 666 in numerical analysis, and AMSC 660 and AMSC 661 in scientific computing. Students must have completed one graduate level course in partial differential equations or one graduate level course in numerical analysis or scientific computing.
Sources
- Course catalogue ↗2026-2027