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Article
Multigrid Convergence for Second Order Elliptic Problems with Smooth Complex Coefficients
Mathematics and Statistics Faculty Publications and Presentations
  • Jay Gopalakrishnan, Portland State University
  • Joseph E. Pasciak, Texas A & M University - College Station
Document Type
Post-Print
Publication Date
1-1-2008
Subjects
  • Finite element method,
  • Numerical analysis,
  • Differential equations
Abstract
The finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither Hermitian nor definite when the coefficient function is complex valued. For such problems, under a uniqueness assumption, we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero. Then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number, providing an efficient solver for computing discrete approximations. Numerical experiments, while confirming the theory, also reveal pronounced sensitivity of Gauss-Seidel iterations on the ordering of the unknowns for certain problems.
Description

NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics & Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics & Engineering, Vol. 197 Issue 49/50, September 2008.

DOI
10.1016/j.cma.2008.05.018
Persistent Identifier
http://archives.pdx.edu/ds/psu/10704
Citation Information
Jay Gopalakrishnan and Joseph E. Pasciak. "Multigrid Convergence for Second Order Elliptic Problems with Smooth Complex Coefficients" (2008)
Available at: http://works.bepress.com/jay-gopalakrishnan/51/