Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials

H. G. Radwan*, P. Vignal, N. Collier, L. Dalcin, M. Santillana, V. M. Calo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we describe the diffusive shallow water equation (DSW) and discuss a numerical strategy to solve it using the generalized-?? method as a method for temporal discretization. This method provides a good norm estimate of the error and guarantees an optimal convergence rate for the spatial discretization. We also discuss the effect of higher polynomial orders on the convergence rates, focusing on the nonlinear DSW problem. Our numerical experiments show that optional convergence rates can be obtained for polynomial orders 1 through 4.

Original languageEnglish (US)
Pages (from-to)160-168
Number of pages9
JournalJournal of the Serbian Society for Computational Mechanics
Volume6
Issue number1
StatePublished - 2012

Keywords

  • Barenblatt solutions
  • Convergence rates
  • DSW
  • Shallow water

ASJC Scopus subject areas

  • Computational Mechanics

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