變分不等式的適應性有限元法逼近

Abstract

我們將適應性有限元法應用在橢圓變分不等式上, 整個程序是基於SOR,弱 餘型估計子, 1-irregular mesh的結合. 我們以數個數值結果顯示此法的 效率性與可靠性. An adaptive approach is developed for finite element approximations of a class of elliptic variational inequalities. The adaptive procedure is based on the SOR method, a weak- residual type of a posteriori error estimation for the computed finite element solutions, and the 1-irregular mesh refinement scheme. Various model problems arising from such as fluid flow in a porous medium, obstacles problems, and semiconductor device simulation are cast into a generic variatiional formulation in terms of approximation as well as error estimation. Reliability of the local error estimators and hence the computed solutions will be illustiated by some numerical experiments. Special attention is paid to the efficient resolution of the geometries in these model problems.