Journal
APPLIED NUMERICAL MATHEMATICS
Volume 59, Issue 6, Pages 1303-1321Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2008.08.005
Keywords
Immersed finite elements; Higher order methods; Discontinuous coefficients
Categories
Funding
- NSF [DMS-0713763]
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In this manuscript we present a p-th degree immersed finite element method for solving boundary value problems with discontinuous coefficients. In this method, interface jump conditions are employed in the finite element basis functions, and the mesh does not have to be aligned with coefficient discontinuity. We show that under h refinement the immersed finite element solution converges to the true solution at the optimal O(h(p+1)) and O(h(p)) rates in the L-2 and H-1 norms, respectively. Furthermore, numerical results suggest that the immersed finite element solution converges exponentially fast under p refinement. Numerical examples are provided to illustrate features of this immersed finite element method. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.
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