Higher-order time domain boundary elements for elastodynamics -- graded meshes and hp versions

Abstract

The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for polygonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.

arXiv comment53 pages, 17 figures, to appear in Numerische Mathematik

References in corpus (7)

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Cited by in corpus (4)

• Time domain boundary elements for elastodynamic contact
• Space-time boundary elements for frictional contact in elastodynamics
• Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions
• Space-time stochastic Galerkin boundary elements for acoustic scattering problems