单调型非线性椭圆问题的边残量型后验误差估计

A Posteriori Error Estimates of Edge Residual Type of Finite Element Method for Monotone Nonlinear Elliptic Problems

摘要:

对于单调型非线性椭圆问题，研究了线性协调有限元的边残量型后验误差估计. 在真解 仅具有H1 正则性的情况下，证明了边残量在后验误差估计中是占优的，并得到了可计算的自适应有限元误差在H1 -范数意义下的上下界. 不计高阶项，边残量可作为线性协调有限元的后验误差估计子. 数值算例验证了该边残量型后验误差估计子的有效性.

Abstract:

The edge residual-based a posteriori error estimates of conforming linear finite element method are studied for the monotone nonlinear elliptic problems. Under the assumption of u \in H1，we prove that the edge residuals dominate a posteriori error estimates, and obtain the computable global upper and local lower bounds on the error of the adaptive finite element method in H1 -norm. Up to higher order terms, edge residuals can be a posteriori error estimators. Numerical examples show the efficiency of the edge residual-based a posteriori error estimators.