• Lecture 1
  • Logistics, introduction, course goals, review of some numerical methods
• Lecture 2
  • Introduction to finite element method, 1D Poisson problem
• Lecture 3
  • Introduction to 2D problems, Banach, Hilbert, and Sobolev spaces
• Lecture 4
  • Trace theorem, variational formulation (precise version), practical/algorithmic aspects
• Lecture 5
  • Riesz representation theorem, abstract formulation for elliptic problems, discretization and error estimates, unisolvence
• Lecture 6
  • Sparse matrices, algorithms, CSR format
• Lecture 7
  • Polynomial interpolation and approximation theory
• Lecture 8
  • Duality argument, pure Neumann conditions
• Lecture 9
  • Linear solvers, stationary methods

These training materials were developed as part of activities under RTG grant DMS-2136228.