- Tytuł:
- An Improved XFEM for the Poisson Equation with Discontinuous Coefficients
- Autorzy:
- Stąpór, P.
- Powiązania:
- https://bibliotekanauki.pl/articles/140045.pdf
- Data publikacji:
- 2017
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
Poisson equation
weak discontinuity
extended finite element method
XFEM
równanie Poissona
słaba nieciągłość
rozszerzona metoda elementów skończonych - Opis:
- 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.
- Źródło:
-
Archive of Mechanical Engineering; 2017, LXIV, 1; 123-144
0004-0738 - Pojawia się w:
- Archive of Mechanical Engineering
- Dostawca treści:
- Biblioteka Nauki
Artykuł