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Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates

By Anders Logg

Abstract

The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution. In this paper, we prove general order a priori error estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution. The estimates then follow from interpolation estimates, together with stability estimates for the discrete dual solution

Topics: Mathematics - Numerical Analysis, 65L05, 65L07, 65L20, 65L50, 65L60, 65L70
Publisher: 'Society for Industrial & Applied Mathematics (SIAM)'
Year: 2012
DOI identifier: 10.1137/040604133
OAI identifier: oai:arXiv.org:1205.2995

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