The hp-version of the boundary element method with quasi-uniform meshes for weakly singular operators on surfaces

Autor:	Alexei Bespalov, Norbert Heuer
Rok vydání:	2008
Předmět:	Applied Mathematics General Mathematics Numerical analysis Mathematical analysis Geometry Computational Mathematics Singular function Rate of convergence Singular solution Norm (mathematics) Degree of a polynomial Laplace operator Boundary element method Mathematics
Zdroj:	IMA Journal of Numerical Analysis. 30:377-400
ISSN:	1464-3642 0272-4979
DOI:	10.1093/imanum/drn052
Popis:	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 ).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b9c3ccf8940eafbb01b58985a534e61e https://doi.org/10.1093/imanum/drn052 Zobrazit plný text záznamu