Wavelet Based Finite Element Methods

In spite of its undeniable success the finite element method suffers from several shortcomings when it comes to the treatment of problems of nonlinear solid mechanics, especially those involving material failure, which often exhibit a high degree of localization, rendering the solution of those problems time intensive and costly. Wavelets, a new class of function systems which only has been developed recently, offer promising features like orthogonality and multiscale resolution, which should allow to resolve the difficulties mentioned above by establishing effective adaptive numerical schemes. The aim of the planned research is to develop adaptive wavelet based finite element algorithms for various nonlinear materials. The novel algorithms will be implemented as computer programs on successively higher levels of complexity while continuously being tested on suitable benchmark problems.