Finite Elements Methods

Contents: Variational formulation of boundary value problems. Lax Milgram Lemma and applications. The Ritz-Galerkin method. Finite element basis functions. Assembly of the Ritz-Galerkin method system, error analysis. Direct and iterative methods for solving finite element equations. Application to Planar Elasticity. Mixed methods, application to Stokes and Maxwell equations. Multidomains formulation. Substructuring and Schwarz method. Application with FreeFem and CATIA codes. Introduction to MPI (Message Passing Interface).