Abstract
We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting of two disjoint domains. We consider the Finite Element Method in the bounded domains to simulate possibly non-linear materials. The Boundary Element Method is applied in unbounded or thin domains where the material behavior is linear. The isogeometric framework allows to combine different design and analysis tools: first, we consider the same type of NURBS parameterizations for an exact geometry representation and second, we use the numerical analysis for the Galerkin approximation. Moreover, it facilitates to perform h- and p-refinements. For the sake of analysis, we consider the framework of strongly monotone and Lipschitz continuous operators to ensure well-posedness of the coupled system. Furthermore, we provide a priori error estimates. We additionally show an improved convergence behavior for the errors in functionals of the solution that may double the rate under certain assumptions. Numerical examples conclude the work which illustrate the theoretical results.
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Open Access funding enabled and organized by Projekt DEAL. The research of Mehdi Elasmi was supported in parts by the Excellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering at TU Darmstadt.
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Communicated by: Long Chen
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Elasmi, M., Erath, C. & Kurz, S. Non-symmetric isogeometric FEM-BEM couplings. Adv Comput Math 47, 61 (2021). https://doi.org/10.1007/s10444-021-09886-3
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DOI: https://doi.org/10.1007/s10444-021-09886-3
Keywords
- Finite element method
- Boundary element method
- Non-symmetric coupling
- Isogeometric analysis
- Non-linear operators
- Laplacian interface problem
- Boundary value problems
- Multiple domains
- Well-posedness
- a priori estimate
- Super-convergence
- Electromagnetics
- Electric machines
Mathematics Subject Classification (2010)
- 65N12
- 65N30
- 65N38
- 78M10
- 78M15