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

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Authors
Radwan, H.
Vignal, P.
Collier, N.
Dalcin, L.
Santillana, M.
Calo, Victor
Date
2012
Type
Journal Article

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Radwan, H. and Vignal, P. and Collier, N. and Dalcin, L. and Santillana, M. and Calo, V. 2012. Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials. Journal of the Serbian Society for Computational Mechanics. 6 (1): pp. 160-168.
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Journal of the Serbian Society for Computational Mechanics
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Department of Applied Geology
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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.