Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.

JO - Archive of Mechanical Engineering L1 - http://sd.czasopisma.pan.pl/Content/104226/PDF/ame-2017-0008.pdf L2 - http://sd.czasopisma.pan.pl/Content/104226 IS - No 1 EP - 144 KW - Poisson equation KW - weak discontinuity KW - XFEM ER - A1 - Stąpór, Paweł PB - Polish Academy of Sciences, Committee on Machine Building VL - vol. 64 JF - Archive of Mechanical Engineering SP - 123 T1 - An improved XFEM for the Poisson equation with discontinuous coefficients UR - http://sd.czasopisma.pan.pl/dlibra/docmetadata?id=104226 DOI - 10.1515/meceng-2017-0008