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

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

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	160-168
Number of pages	9
Journal	Journal of the Serbian Society for Computational Mechanics
Volume	6
Issue number	1
State	Published - 2012
Externally published	Yes

Keywords

Barenblatt solutions
Convergence rates
DSW
Shallow water

Cite this

@article{8c4737f516aa4663b46d7f164fd1e69c,

title = "Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials",

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.",

keywords = "Barenblatt solutions, Convergence rates, DSW, Shallow water",

author = "Radwan, {H. G.} and P. Vignal and N. Collier and L. Dalcin and M. Santillana and Calo, {V. M.}",

year = "2012",

language = "English",

volume = "6",

pages = "160--168",

journal = "Journal of the Serbian Society for Computational Mechanics",

issn = "1820-6530",

number = "1",

}

TY - JOUR

T1 - Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials

AU - Radwan, H. G.

AU - Vignal, P.

AU - Collier, N.

AU - Dalcin, L.

AU - Santillana, M.

AU - Calo, V. M.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Barenblatt solutions

KW - Convergence rates

KW - DSW

KW - Shallow water

UR - http://www.scopus.com/inward/record.url?scp=84872870266&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84872870266

SN - 1820-6530

VL - 6

SP - 160

EP - 168

JO - Journal of the Serbian Society for Computational Mechanics

JF - Journal of the Serbian Society for Computational Mechanics

IS - 1

ER -

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

Abstract

Keywords

Other files and links

Fingerprint

Cite this