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A posteriori L8(L2)-error bounds for finite element approximations to the wave equation

journal contribution
posted on 2023-06-08, 15:50 authored by Emmanuil H Georgoulis, Omar LakkisOmar Lakkis, Charalambos Makridakis
We address the error control of Galerkin discretization (in space) of linear second-order hyperbolic problems. More specifically, we derive a posteriori error bounds in the L8(L2) norm for finite element methods for the linear wave equation, under minimal regularity assumptions. The theory is developed for both the space-discrete case and for an implicit fully discrete scheme. The derivation of these bounds relies crucially on carefully constructed space and time reconstructions of the discrete numerical solutions, in conjunction with a technique introduced by Baker (1976, Error estimates for finite element methods for second-order hyperbolic equations. SIAM J. Numer. Anal., 13, 564--576) in the context of a priori error analysis of Galerkin discretization of the wave problem in weaker-than-energy spatial norms.

History

Publication status

  • Published

File Version

  • Published version

Journal

IMA Journal of Numerical Analysis

ISSN

0272-4979

Publisher

Oxford University Press

Issue

4

Volume

33

Page range

1245-1264

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-09-19

First Compliant Deposit (FCD) Date

2013-09-18

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