Numerical approximations of singular source terms in differential equations
2004 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 200, no 2, 462-488 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2004. Vol. 200, no 2, 462-488 p.
immersed boundary method, front-tracking method, flow
IdentifiersURN: urn:nbn:se:kth:diva-23828DOI: 10.1016/j.jcp.2004.04.011ISI: 000224653100004OAI: oai:DiVA.org:kth-23828DiVA: diva2:342527
QC 201005252010-08-102010-08-10Bibliographically approved