A Fixed Grid Finite Element Method for Elliptic Interface Problems
2006 (English)In: Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, 2006, 1-23 p.Conference paper (Refereed)
A finite element method for two-dimensional elliptic interface problem is presented. Due to the presence of these interfaces the problem will contain discontinuities in the coefficients and singular source terms that are represented by delta functions along the interface. As a result, the solution to the interface problem and its deratives may have jump discontinuities. The new method is specifically designed to handle this feature of the solution in the context of non-interface fitted grids.
The main idea is to modify the standard basis function in the vicinity of the interface such that the jump conditions are well approximated. The resulting finite element space is, in general, non-conforming. The interface itself is represented by a set of Lagrangian markers together with a parametric description connecting them. To illustrate the abilities of the method, numerical tests are presented. For all the considered test problems, the new method has been shown to have super-linear or second order of convergence. Our approach is also compared with the standard finite element method. Finally, the method has been successfully applied to the Stokes interface problems.
Place, publisher, year, edition, pages
2006. 1-23 p.
elliptic equations; finite element method; interface; singular source term; discontinous coefficients; immersed interface method
IdentifiersURN: urn:nbn:se:kth:diva-7561OAI: oai:DiVA.org:kth-7561DiVA: diva2:12626
the International Conference on Numerical Analysis and Applied Mathematics, ICNAAM, Greece, 2006
QC 201008062007-10-232007-10-232010-08-06Bibliographically approved