Highly accurate finite element method for one-dimensional elliptic interface problems
2009 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, no 1, 119-134 p.Article in journal (Refereed) Published
A high order finite element method for one-dimensional elliptic interface problems is presented. Due to presence of these interfaces the problem will contain discontinuities in the coefficients and singularities in the right hand side that are represented by delta functional with the support on the interfaces. As a result, the solution to the interface problem and its derivatives may have jump discontinuities. The proposed method is specifically designed to handle this features of the solution using non-body fitted grids, i.e. the grids are not aligned with the interfaces.The finite element method will be based on third order Hermitian interpolation. The main idea is to modify the basis functions in the vicinity of the interface such that the jump conditions are well approximated. A rigorous error analysis shows that the presented finite element method is fourth order accurate in L-2 norm. The numerical results agree well with the theoretical analysis. The basic idea can easily be generalized to other finite element ansatz functions.
Place, publisher, year, edition, pages
2009. Vol. 59, no 1, 119-134 p.
Discontinuous coefficients; Elliptic interface problem; Finite element method; Immersed interface method; Singular source; Electric network analysis; Error analysis; Probability density function; Problem solving; Basic ideas; Basis functions; Discontinuous coefficients; Elliptic interface problem; Elliptic interface problems; Finite elements; Fourth orders; Hermitian; High order finite element methods; Immersed interface method; Interface problems; Jump conditions; Jump discontinuities; Numerical results; Right hands; Singular source; Theoretical analyses; Third orders
IdentifiersURN: urn:nbn:se:kth:diva-7562DOI: 10.1016/j.apnum.2007.12.003ISI: 000261485800007ScopusID: 2-s2.0-55149091553OAI: oai:DiVA.org:kth-7562DiVA: diva2:12627
QC 20100806. Uppdaterad från Submitted till Published 20100806.2007-10-232007-10-232010-08-06Bibliographically approved