127 research outputs found
A Nitsche-based domain decomposition method for hypersingular integral equations
We introduce and analyze a Nitsche-based domain decomposition method for the
solution of hypersingular integral equations. This method allows for
discretizations with non-matching grids without the necessity of a Lagrangian
multiplier, as opposed to the traditional mortar method. We prove its almost
quasi-optimal convergence and underline the theory by a numerical experiment.Comment: 21 pages, 5 figure
Natural hp-BEM for the electric field integral equation with singular solutions
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 page
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