Communications in Mathematical Sciences

Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrov-Galerkin Formulation

Thomas Y. Hou, Xiao-Hui Wu, and Yu Zhang

Abstract

We continue the study of the nonconforming multiscale finite element method (Ms-FEM) introduced in [17, 14] for second order elliptic equations with highly oscillatory coefficients. The main difficulty in MsFEM, as well as other numerical upscaling methods, is the scale resonance effect. It has been show that the leading order resonance error can be effectively removed by using an over-sampling technique. Nonetheless, there is still a secondary cell resonance error of O(e2h2). Here, we introduce a Petrov-Galerkin MsFEM formulation with nonconforming multiscale trial functions and linear test functions. We show that the cell resonance error is eliminated in this formulation and hence the convergence rate is greatly improved. Moreover, we show that a similar formulation can be used to enhance the convergence of an immersed-interface finite element method for elliptic interface problems.

Article information

Source
Commun. Math. Sci. Volume 2, Number 2 (2004), 185-205.

Dates
First available in Project Euclid: 1 March 2005

Permanent link to this document
http://projecteuclid.org/euclid.cms/1109706534

Mathematical Reviews number (MathSciNet)
MR2119937

Zentralblatt MATH identifier
1085.65109

Citation

Hou, Thomas Y.; Wu, Xiao-Hui; Zhang, Yu. Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrov-Galerkin Formulation. Communications in Mathematical Sciences 2 (2004), no. 2, 185--205. http://projecteuclid.org/euclid.cms/1109706534.


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