An Improved XFEM for the Poisson Equation with Discontinuous Coefficients

• Autorzy: Stąpór P.

Identyfikatory

DOI

10.1515/meceng-2017-0008

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Poisson equation; weak discontinuity; extended finite element method; XFEM

PL

równanie Poissona; słaba nieciągłość; rozszerzona metoda elementów skończonych; XFEM

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2017
• Tom: Vol. LXIV, nr 1
• Strony: 123--144
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Stąpór P.

• Kielce University of Technology, Faculty of Management and Computer Modelling, Al. Tysiąclecia Panstwa Polskiego 7, 25-314 Kielce, Poland

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).