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Finite elements with mesh refinement for elastic wave propagation in polygons
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 G⊂R² inline image 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 Show more
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Journal / seriesResearch Report
Organisational unit03435 - Schwab, Christoph
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