用有限元亏量校正求特征值下界

A Finite Element Defect Correction Scheme and Lower Bounds for the Eigenvalue

对解2阶椭圆特征值问题的线性有限元法,本文考虑了一种计算简单的有限元亏量校正方案。基于插值校正和Rayleigh商给出了新的校正特征值。理论分析表明该校正特征值或者达到二次元的精度阶或者当网格直径充分小时下逼近准确特征值,并用数值实验验证了理论结果。

This paper considers a kind of finite element defect correction scheme which possesses low computing complexities for the linear finite element method solving the second-order elliptic eigenvalue problem, Based on the interpolated correction and the Rayleigh quotient, a new corrected eigenvalue is obtained. Theoretical analysis shows the corrected eigenvalue either achieves the convergence order of the quadratic finite element eigenvalue, or approximates the accurate eigenvalue from the below as the mesh size sufficiently small. Numerical experiments are provided to support our theoretical conclusions.