Finite elements with mesh refinement for elastic wave propagation in polygons
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- 作者：Fabian Mü ; ller and Christoph Schwab
- 刊名：Mathematical Methods in the Applied Sciences
- 出版年：2016
- 出版时间：30 November 2016
- 年：2016
- 卷：39
- 期：17
- 页码：5027-5042
- 全文大小：445K
- ISSN：1099-1476
文摘
Error estimates for the space-semidiscrete finite element approximation of solutions to initial boundary value problems for linear, second-order hyperbolic systems in bounded polygons with straight sides are presented. Using recent results on corner asymptotics of solutions of linear wave equations with time-independent coefficients in conical domains, it is shown that continuous, simplicial Lagrangian finite elements of uniform polynomial degree p≥1, with either suitably graded mesh refinement or with bisection-tree mesh refinement toward the corners of G, achieve the (maximal) asymptotic rate of convergence O(N−p/2), where N denotes the number of degrees of freedom spent for the finite element space semidiscretization. In the present analysis, Dirichlet, Neumann and mixed boundary conditions are considered. Numerical experiments that confirm the theoretical results are presented for linear elasticity. Copyright