On solving singular interface problems using the enriched partition-of-unity finite element methods
Lee, Chi King
Fan, Sau Cheong
Date of Issue2003
School of Civil and Environmental Engineering
It has been well recognized that interface problems often contain strong singularities which make conventional numerical approaches such as uniform h- or p-version of finite element methods inefficient. In this paper, the partition-of-unity finite element method (PUFEM) is applied to obtain solution for interface problems with severe singularities. In the present approach, asymptotical expansions of the analytical solutions near the interface singularities are employed to enhance the accuracy of the solution. Three different enrichment schemes for interface problems are presented, and their performances are studied. Compared to other numerical approaches such as h-p version of finite element method, the main advantages of the present method include (i) easy and simple formulation, (ii) highly flexible enrichment configurations, (iii) no special treatment needed for numerical integration and boundary conditions and (iv) highly effective in terms of computational efficiency. Numerical examples are included to illustrate the robustness and performance of the three schemes in conjunction with uniform h- or p-refinements. It shows that the present PUFEM formulations can significantly improve the accuracy of solution. Very often, improved convergence rate is obtained through enrichment in conjunction with p-refinement.
DRNTU::Engineering::Civil engineering::Structures and design
© 2003 Emerald Group Publishing Limited. This is the author created version of a work that has been peer reviewed and accepted for publication by Engineering Computations, Emerald Group Publishing Limited. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [Article DOI: http://dx.doi.org/10.1108/02644400310502991].