Multimesh finite element methods: solving PDEs on multiple intersecting meshes. (English) Zbl 1440.65214
Summary: We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology.
In the accompanying paper [“Multimesh finite elements with flexible mesh sizes”, Preprint, arXiv:1804.06455], we analyze the proposed method and prove optimal order convergence and stability.
In the accompanying paper [“Multimesh finite elements with flexible mesh sizes”, Preprint, arXiv:1804.06455], we analyze the proposed method and prove optimal order convergence and stability.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
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