Affiliation:
1. Department of Mathematics, University of Athens, 15784 Zographou, Greece, and Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece
Abstract
Abstract
We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension. We discretize the problem in space by the standard Galerkin finite element method on a quasiuniform mesh and in time by the classical four-stage, fourth order, explicit Runge–Kutta scheme. Assuming smoothness of solutions, a Courant number restriction and certain hypotheses on the finite element spaces, we prove $L^{2}$ error estimates that are of fourth-order accuracy in the temporal variable and of the usual, due to the nonuniform mesh, suboptimal order in space. We also make a computational study of the numerical spatial and temporal orders of convergence, and of the validity of a hypothesis made on the finite element spaces.
Funder
Innovative Actions in Environmental Research and Development
Operational Program ‘Competitiveness, and Innovation’
European Regional Development Fund
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,General Mathematics
Cited by
3 articles.
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