Articulo
Discontinuous Petrov-Galerkin boundary elements
Numerische Mathematik
Registro en:
1150056
1150056
Autor
Heuer, Norbert
Karkulik, Michael
Institución
Resumen
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in Heuer and Pinochet (SIAM J Numer Anal: 52(6), 2703-2721, 2014), we study the case of a hypersingular integral equation on open and closed polyhedral surfaces. We develop a general ultra-weak setting in fractional-order Sobolev spaces and prove its well-posedness and equivalence with the traditional formulation. Based on the ultra-weak formulation, we establish a discontinuous Petrov-Galerkin method with optimal test functions and prove its quasi-optimal convergence in related Sobolev norms. For closed surfaces, this general result implies quasi-optimal convergence in the L-2-norm. Some numerical experiments confirm expected convergence rates. Keywords. KeyWords Plus:WEAK VARIATIONAL FORMULATION DOMINATED DIFFUSION-PROBLEMS PRACTICAL DPG METHOD LINEAR ELASTICITY LIPSCHITZ-DOMAINS EQUATION APPROXIMATION MATRICES NORMS Regular 2015 FONDECYT FONDECYT