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The proposed project is a free continuation of the grant Finite element method for three-dimensional problems IAA1019201, which terminated in 2006 and which was fulfilled with excellent results. The main goal of the new project will be a thorough mathematical and numerical analysis of the finite element method for solving partial differential equations in higher dimensional spaces. The necessity of solving such problems arises, e.g., in theory of relativity, statistical and particle physics, financial mathematics. In particular, we would like to deal with generation of simplicial meshes of polytopic domains. Further, we will investigate the existence and uniqueness of continuous and approximate solutions of problems that are often nonlinear. A special emphasize will be laid also on a priori and a posteriori error estimates, superconvergence, discrete maximum principle, stability of numerical schemes, etc.
Main investigators:
Participating institutions:
Institute of Mathematics AS CR
