半线性椭圆问题的非精确自适应有限元方法

The Inexact Adaptive Finite Element Method for Semilinear Elliptic Problems

考虑一类半线性椭圆问题的非精确自适应有限元方法.该算法在初始网格需要精确求解,而在其余网格只需要对上一步的近似解进行一次牛顿更新.利用有限元方法的精确解和非精确解之间的超逼近性质,给出该方法的先验和后验误差估计,最后通过具体算例来验证该理论的正确性和该方法的有效性.

A type of inexact adaptive finite element method for semilinear elliptic problems is considered.The algorithm needs an accurate solution on the coarsest level,and the remaining levels involve only single Newton updates to the previous approximate solution.By using the super approximation property between the exact and inexact solutions of finite element method,the priori and posteriori error estimates of the proposed method are given,and the numerical experiments are provided to illustrate the theory and the algorithm.