Abstract: 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.
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DOI 
YADDA/CEON