A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems
| Autor: | Mingchao Cai, Fangfang Qin, Zhilin Li, Jinru Chen |
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| Rok vydání: | 2017 |
| Předmět: |
Approximation property
Mathematical analysis Geometry 010103 numerical & computational mathematics Mixed finite element method 01 natural sciences Finite element method law.invention Regular grid 010101 applied mathematics Computational Mathematics Planar Computational Theory and Mathematics law Modeling and Simulation Norm (mathematics) Polygon mesh Cartesian coordinate system 0101 mathematics Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 73:404-418 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2016.11.033 |
| Popis: | In this paper, a new nonconforming immersed finite element (IFE) method on triangular Cartesian meshes is developed for solving planar elasticity interface problems. The proposed IFE method possesses optimal approximation property for both compressible and nearly incompressible problems. Its degree of freedom is much less than those of existing finite element methods for the same problem. Moreover, the method is robust with respect to the shape of the interface and its location relative to the domain and the underlying mesh. Both theory and numerical experiments are presented to demonstrate the effectiveness of the new method. Theoretically, the unisolvent property and the consistency of the IFE space are proved. Experimentally, extensive numerical examples are given to show that the approximation orders in L2 norm and semi-H1 norm are optimal under various Lam parameters settings and different interface geometry configurations. |
| Databáze: | OpenAIRE |
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