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A new hybrid velocity integration method applied to elastic wave propagation
Author(s) -
Chen Zhiyun,
Steeb Holger,
Diebels Stefan
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2167
Subject(s) - discretization , mathematics , galerkin method , convergence (economics) , mathematical analysis , displacement (psychology) , a priori and a posteriori , field (mathematics) , vector field , displacement field , discontinuous galerkin method , finite element method , geometry , physics , psychology , philosophy , epistemology , pure mathematics , economics , psychotherapist , thermodynamics , economic growth
We present a novel space–time Galerkin method for solutions of second‐order time‐dependent problems. By introducing the displacement–velocity relationship implicitly, the governing set of equations is reformulated into a first‐order single field problem with the unknowns in the velocity field. The resulting equation is in turn solved by a time‐discontinuous Galerkin approach ( Int. J. Numer. Anal. Meth. Geomech . 2006; 30 :1113–1134), in which the continuity between time intervals is weakly enforced by a special upwind flux treatment. After solving the equation for the unknown velocities, the displacement field quantities are computed a posteriori in a post‐processing step. Various numerical examples demonstrate the efficiency and reliability of the proposed method. Convergence studies with respect to the h ‐ and p ‐refinement and different discretization techniques are given. Copyright © 2007 John Wiley & Sons, Ltd.