[Winter 1999 Colloquiums]
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COLLOQUIUM

DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309

Daoqi Yang
Department of Mathematics
Wayne State University

Finite Elements for Elliptic Interface Problems with
Strongly Discontinuous Coefficients and Solutions

Abstract

An iterative finite element algorithm is proposed for numerically solving two-phase steady-state generalized Stefan interface problems with discontinuous solutions, conormal derivatives, and coefficients. This algorithm employs finite element methods and iteratively solves smaller subregion problems for each phase with good accuracy, and exchanges information at the interface to advance the iteration. The finite element grids in different phases do not have to match each other at the interface. Numerical experiments are performed to show the accuracy and efficiency of the algorithm for capturing discontinuities in the solutions and coefficients. One surprising property of the algorithm is that its accuracy does not deteriorate as the discontinuity in the coefficients becomes worse. That is, the accuracy remains the same for continuous problems and strongly discontinuous problems. Another surprising property is that its conditioning becomes better as the discontinuity gets worse. In other words, the stronger the discontinuity, the faster convergence. Numerical examples on matching and non-matching unstructured grids are given with coefficient discontinuity jumps in the order of 10³, 10⁵, 10¹⁰, 10⁵⁰ and 10¹⁰⁰.

372 Science and Engineering Building
Tuesday, April 13, 1999
3:00-4:00 P.M.

Refreshments at 2:30-3:00 PM in Room 368, Science and Engineering Building