Error estimation for immersed interface solutions

Ben A. Vanderlei; Matthew M. Hopkins; Lisa J. Fauci

doi:10.3934/dcdsb.2012.17.1185

Article Contents

2012, Volume 17, Issue 4: 1185-1203. Doi: 10.3934/dcdsb.2012.17.1185

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Error estimation for immersed interface solutions

1.
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2
2.
Nanoscale and Reactive Processes, Sandia National Laboratories, Albuquerque, NM 87185-0836
3.
Department of Mathematics, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118

Received: August 31, 2010

Revised: July 31, 2011

Published: May 2012

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Abstract

We present an error estimation method for immersed interface solutions of elliptic boundary value problems. As opposed to an asymptotic rate that indicates how the errors in the numerical method converge to zero, we seek a posteriori estimates of the errors, and their spatial distribution, for a given solution. Our estimate is based upon the classical idea of defect corrections, which requires the application of a higher-order discretization operator to a solution achieved with a lower-order discretization. Our model problem will be an elliptic boundary value problem in which the coefficients are discontinuous across an internal boundary.

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Mathematics Subject Classification: Primary: 65N22, 65N06; Secondary: 82B24.

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