A weighted least squares finite element method for elliptic problems with degenerate and singular coefficients
A weighted least squares finite element method for elliptic problems with degenerate and singular coefficients
复制标题
求解简并奇异系数椭圆问题的加权最小二乘有限元法
作者：
S. Bidwell;M. Hassell;C. Westphal
考虑二阶椭圆型偏微分方程，其系数在区域的内点处为奇异或简并。本文给出了这类问题的一种新的加权范数最小二乘有限元方法的表述和分析。我们提出了一种加权方案来消除污染效应并恢复最优收敛速率。理论结果在适当加权的Sobolev空间中进行，包括加权齐次最小二乘泛函的椭圆性界、椭圆算子的正则性界和误差估计。数值实验证实了预测的误差范围。
We consider second order elliptic partial differential equations with coefficients that are singular or degenerate at an interior point of the domain. This paper presents formulation and analysis of a novel weighted-norm least squares finite element method for this class of problems. We propose a weighting scheme that eliminates the pollution effect and recovers optimal convergence rates. Theoretical results are carried out in appropriately weighted Sobolev spaces and include ellipticity bounds on the weighted homogeneous least squares functional, regularity bounds on the elliptic operator, and error estimates. Numerical experiments confirm the predicted error bounds.