Finite element hp-methods for partial differential equations

Abstract

We deal with the numerical solution of partial differential equations using finite element method whose mathematical background was built in 60's by prof. Zlámal. We focus on the hp-mesh adaptive methods that combine the refinement of mesh elements and the variation of the degree of polynomial approximation. The hp-method can give the exponential rate of convergence of the error with respect to the number of degrees of freedom. We present several theoretical results, which are supported by numerical experiments.