An Iterative Hybridized Mixed Finite Element Method for Elliptic Interface Problems with Strongly Discontinuous Coefficients
Year: 2003
Author: Dao-Qi Yang, Jennifer Zhao
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 3 : pp. 257–276
Abstract
An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions, conormal derivatives, and coefficients. This algorithm iteratively solves small problems for each single phase with good accuracy and exchange information at the interface to advance the iteration until convergence, following the ideal of Schwarz Alternating Methods: Error estimates are derived to show that this algorithm always converges provided that relaxation parameters are suitably chosen. Numerical experiments with matching and non-matching grids at the interface from different phases are performed to show the accuracy of the method for capturing discontinuities in the solutions and coefficients. In contrast to standard numerical methods, the accuracy of our method does not seem to deteriorate as the coefficient discontinuity increases.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-8878
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 3 : pp. 257–276
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Mixed finite element method Interface problems Discontinuous solutions.