MATH 610
Numerical Methods in Partial Differential Equations

Notes

Preliminaries

• Sobolev spaces

Finite Difference Methods

• Finite difference methods
• Analysis of an upwind finite difference scheme

Finite Element Methods

• Finite element triples
• Unisolvence of finite element triples
• 2d finite element methods
• Computing the error of 2d finite element methods
• A proof of Strang’s first lemma
• Duality arguments in finite element error analysis