多维问题有限元逼近的误差展式及其应用 ——Ⅰ.特征值问题

Finite Element Error Expansions for Multidimensional Prob- lems and Their Applications I. Eigenvalue Problem

对于多维区域Ω~R^X(N＞2),采用适当的单元剖分。给出Ω上特征值问题的有限元逼近的渐近误差展式,从而从理论上说明通过Richardson外推。可以将计算精度从二阶提高到四阶。

For the eigenvalue problem on multidimensional domain Ω~R^X(N>2) the discrete eigenvalue with finite elements is shown to admit asymptotic error expansions on ecrtain meshes. This provies the theoretical justification for the use of Richardson extrapolation for increasing the accuracy from second to fourth order.