二阶椭圆方程自适应最小二乘混合有限元法

An Adaptive Least-squares Mixed Finite Element Method for Second Order Elliptic Equations

研究了二阶椭圆方程的自适应最小二乘混合有限元法,利用二次非协调有限元空间和Raviatr-Thomas有限元空间进行逼近,利用最小二乘函数构造了进行自适应计算的后验误差估计子,并进行了后验误差估计。

A least squares mixed finite element method for the numerical solution of second order elliptic equations is analyzed and developed in this paper. The quadratic nonconforming and Raviart-Thomas finite element spaces are used to approximate. The aposteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated.