Sobolev方程的等参有限元法

Isoparametric Finite Element Method to Solve Sobolev Equation

用等参有限元去逼近曲边区域可以使误差阶不受损失,达到和凸多边形区域上同样的收敛阶.本文研究Sobolev方程的等参有限元方法,在半离散和向后欧拉全离散格式下,分别讨论真解和有限元解之间的误差估计,最后用数值算例进一步验证了理论结果.

One of the most advantages about isoparametric finite element method in curved domain is still to preserve convergence order as in convex polygons.In this paper,isoparametric finite element method to solve Sobolev equation is studied.The errors between the true solution and finite element solution are estimated under both semi-discrete scheme and the backward Euler fully discrete scheme respectively.Finally,the given numerical example further illustrates the analytical result.