ORIGINAL PAPER

A Posteriori Error Estimates for Finite Element Methods for Systems of Nonlinear, Dispersive Equations

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  • 1. Department of Mathematics, University of Tennessee, Knoxville, TN, USA;
    2. Advanced Technology Integration Department, Dynetics, Inc., Huntsville, AL, USA

Received date: 2020-08-30

  Revised date: 2021-04-17

  Online published: 2022-07-04

Supported by

This work was supported in part by the National Science Foundation under grant DMS-1620288

Abstract

The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type, coupled through their nonlinear terms. In our previous work [9], we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes. In this sequel, we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in [9]. The key tool employed to effect our analysis is the dispersive reconstruction developed by Karakashian and Makridakis [20] for related discontinuous Galerkin methods. We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.

Cite this article

Ohannes A. Karakashian, Michael M. Wise . A Posteriori Error Estimates for Finite Element Methods for Systems of Nonlinear, Dispersive Equations[J]. Communications on Applied Mathematics and Computation, 2022 , 4(3) : 823 -854 . DOI: 10.1007/s42967-021-00143-4

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