The <i>hp</i>-version of the boundary element method with quasi-uniform meshes for weakly singular operators on surfaces
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2010
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Abstract
We prove an a priori error estimate for the hp-version of the boundary element method with weakly singular operators in three dimensions. The underlying meshes are quasi-uniform. Our model problem is that of the Laplacian exterior to an open surface, where the solution has strong singularities that are not L-2-regular. Our results confirm previously conjectured convergence rates in h (the mesh size) and p (the polynomial degree) and these rates are given explicitly in terms of the exponents of the singular functions. In particular, for sufficiently smooth given data we prove a convergence in the energy norm like O(h(1/2)p(-1)).
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hp-version with quasi-uniform meshes, boundary element method, weakly singular operators, singularities