Natural hp-BEM for the electric field integral equation with singular solutions
| Autor: | Norbert Heuer, Alexei Bespalov |
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| Rok vydání: | 2011 |
| Předmět: |
Surface (mathematics)
Numerical Analysis Applied Mathematics Mathematical analysis Numerical Analysis (math.NA) Electric-field integral equation Lipschitz continuity Mathematics::Numerical Analysis Computational Mathematics Singularity FOS: Mathematics Degree of a polynomial Gravitational singularity Mathematics - Numerical Analysis 65N38 65N15 78M15 41A10 Finite set Boundary element method Analysis Mathematics |
| Zdroj: | Numerical Methods for Partial Differential Equations. 28:1466-1480 |
| ISSN: | 0749-159X |
| DOI: | 10.1002/num.20688 |
| Popis: | We apply the hp-version of the boundary element method (BEM) for the numerical solution of the electric field integral equation (EFIE) on a Lipschitz polyhedral surface G. The underlying meshes are supposed to be quasi-uniform triangulations of G, and the approximations are based on either Raviart-Thomas or Brezzi-Douglas-Marini families of surface elements. Non-smoothness of G leads to singularities in the solution of the EFIE, severely affecting convergence rates of the BEM. However, the singular behaviour of the solution can be explicitly specified using a finite set of power functions (vertex-, edge-, and vertex-edge singularities). In this paper we use this fact to perform an a priori error analysis of the hp-BEM on quasi-uniform meshes. We prove precise error estimates in terms of the polynomial degree p, the mesh size h, and the singularity exponents. Comment: 17 pages |
| Databáze: | OpenAIRE |
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