论文标题
通用有限元方法，用于签名系数问题
A generalized finite element method for problems with sign-changing coefficients
论文作者
论文摘要
例如，在研究超材料的传输问题时，会出现签名改变系数的问题。在这项工作中，我们以局部正交分解的精神介绍并分析了一种通用的有限元方法，当负材料和阳性材料具有多尺度特征时，这尤其有效。我们在能量规范中得出最佳的线性收敛，而与精确溶液的潜在低规律性无关。数值实验说明了理论收敛速率，并显示了该方法在大量签名变化问题上的适用性。
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal Decomposition, that is especially efficient when the negative and positive materials exhibit multiscale features. We derive optimal linear convergence in the energy norm independently of the potentially low regularity of the exact solution. Numerical experiments illustrate the theoretical convergence rates and show the applicability of the method for a large class of sign-changing diffusion problems.
