Non-symmetric isogeometric FEM-BEM couplings

• Published in: Advances in computational mathematics Vol. 47; no. 5
• Main Authors: Elasmi, Mehdi, Erath, Christoph, Kurz, Stefan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2021; Springer Nature B.V
• Subjects: Boundary element method; Boundary value problems; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Couplings; Domains; Finite element method; Mathematical analysis; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Numerical analysis; Operators (mathematics); Visualization; Isogeometric analysis; Boundary value problems; 65N12; Non-linear operators; Laplacian interface problem; 65N38; 78M10; Electromagnetics; Finite element method; 78M15; Electric machines; Multiple domains; Non-symmetric coupling; Super-convergence; Boundary element method; a priori estimate; 65N30; Well-posedness
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-021-09886-3

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.