Metoda kompozitních konečných prvků ve 2 dimenzích

Abstract

Most practical problems that lead to mathematical modelling using partial differential equations (PDE) cannot be solved analytically, instead numerical methods should be applied. One of the main problems for numerical solution of PDE is an approximation of boundary conditions. Discretisation grid must properly represent border of the domain, which leads to large systems of linear equations for practical problems. An alternative method, so called composite finite elements, was proposed in [1]. This method leads to construction of hierarchy of non-conforming grids, which cover the domain with small geometric details [2]. Composite finite element basis functions have bigger supports and the resulting system matrices are more dense, but these systems can be solved efficiently. The aim of this thesis is to construct and solve problems using this method.