A posteriori error estimates for discontinuous Galerkin Methods for the Generalised Korteweg-de Vries Equation

Karakashian, Ohannes and Makridakis, Charalambos (2014) A posteriori error estimates for discontinuous Galerkin Methods for the Generalised Korteweg-de Vries Equation. Mathematics of Computation, 84. pp. 1145-1167. ISSN 0025-5718

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Abstract

We construct, analyze and numerically validate a posteriori error estimates for conservative discontinuous Galerkin (DG) schemes for the Generalized Korteweg-de Vries (GKdV) equation. We develop the concept of dispersive reconstruction, i.e., a piecewise polynomial function which satisfies the GKdV equation in the strong sense but with a computable forcing term enabling the use of a priori error estimation techniques to obtain computable upper bounds for the error. Both semidiscrete and fully discrete approximations are treated.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 24 Jan 2018 10:12
Last Modified: 24 Jan 2018 12:23
URI: http://sro.sussex.ac.uk/id/eprint/73106

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