Numerical PDE and FEM
Question
How do the mathematical assumptions behind a weak formulation appear in the assembled system and its numerical error?
Planned sequence
- Choose a model elliptic problem, boundary conditions, and a manufactured solution.
- State the function spaces, weak formulation, and well-posedness assumptions.
- Derive a finite-element discretization and implement assembly.
- Check boundary treatment, matrix structure, and mesh convergence.
- Pass the assembled system to the solver project.
Evidence to record
Keep the mesh family, element order, quadrature choice, norms, solver tolerance, and observed errors with the exact source commit and run commands. Separate discretization error from algebraic solver error.
Current evidence
This is a planned project. There is no published FEM implementation or convergence table yet. Measure theory notes provide part of the mathematical study background; Sobolev-space notes remain unfinished.
Study prerequisites
Folland Seminar · Linear Algebra → Numerical PDE · Saad → PDE / parallel operations
Linked notes
No project notes have been published yet. The steps above describe planned work.
Linked paper notes
No paper notes linked yet.