Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 200, Issue 2, Pages 462-488Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2004.04.011
Keywords
-
Ask authors/readers for more resources
Singular terms in differential equations pose severe challenges for numerical approximations on regular grids. Regularization of the singularities is a very useful technique for their representation on the grid. We analyze such techniques for the practically preferred case of narrow support of the regularizations, extending our earlier results for wider support. The analysis also generalizes existing theory for one dimensional problems to multi-dimensions. New high order multi-dimensional techniques for differential equations and numerical quadrature are introduced based on the analysis and numerical results are presented. We also show that the common use of distance functions in level-set methods to extend one dimensional regularization to higher dimensions may produce O(1) errors. (C) 2004 Published by Elsevier Inc.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available