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In this program

Weak formulations of elliptic boundary-value problems
Lax–Milgram theorem and well-posedness
Galerkin and Petrov–Galerkin approximations
Energy norms
Best approximation in Hilbert spaces
Abstract error estimates (Céa's lemma)

Variational foundations

Best approximation in Hilbert spaces

Finite element methods · Standard syllabus

Topic

Best approximation in Hilbert spaces

Practice by unit: Variational foundations

Graduate Finite Element Methods — scope drawn from open FEM notes and typical US graduate finite element syllabi.

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