Syllabus
abstract variational problem, Lax-Milgram lemma;
Galerkin approximation, Cea's lemma;
Lagrange and Hermite finite elements, concept of affine equivalence; construction of finite element spaces, satisfaction of stable boundary conditions; approximation theory in Sobolev spaces, application to Lagrange and Hermite interpolation of functions; error estimates for Galerkin approximations in the energy and L2 norm; numerical integration in FEM, errors of quadrature formulas; error of finite element approximation in the presence of numerical integration;
FEM for parabolic problems
Annotation
The aim of this course is to present the mathematical theory of finite element methods and their applications in solving linear elliptic equations. This covers: approximation theory for mappings preserving polynomials , application to the Lagrange and Hermite interpolation of functions in multidimensional space , description of the most frequently used finite elements, the error analysis, numerical integration in FEM.