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CutFEM without cutting the mesh cells: A new way to impose Dirichlet and Neumann boundary conditions on unfitted meshes
- Source :
- Computer Methods in Applied Mechanics and Engineering, Computer Methods in Applied Mechanics and Engineering, Elsevier, 2019, 356, pp.75-100. ⟨10.1016/j.cma.2019.07.008⟩
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- We present a method of CutFEM type for the Poisson problem with either Dirichlet or Neumann boundary conditions. The computational mesh is obtained from a background (typically uniform Cartesian) mesh by retaining only the elements intersecting the domain where the problem is posed. The resulting mesh does not thus fit the boundary of the problem domain. Several finite element methods (XFEM, CutFEM) adapted to such meshes have been recently proposed. The originality of the present article consists in avoiding integration over the elements cut by the boundary of the problem domain, while preserving the optimal convergence rates, as confirmed by both the theoretical estimates and the numerical results.
- Subjects :
- Computer science
Computational Mechanics
General Physics and Astronomy
Boundary (topology)
65N30, 65N85, 65N15
010103 numerical & computational mathematics
01 natural sciences
Domain (mathematical analysis)
law.invention
law
FOS: Mathematics
Neumann boundary condition
Applied mathematics
Polygon mesh
Cartesian coordinate system
Mathematics - Numerical Analysis
0101 mathematics
ComputingMilieux_MISCELLANEOUS
Extended finite element method
Mechanical Engineering
Numerical Analysis (math.NA)
Finite element method
Computer Science Applications
010101 applied mathematics
Mechanics of Materials
Problem domain
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Subjects
Details
- ISSN :
- 00457825
- Volume :
- 356
- Database :
- OpenAIRE
- Journal :
- Computer Methods in Applied Mechanics and Engineering
- Accession number :
- edsair.doi.dedup.....75171226dda58a6ab416776b0afbf718