Finite element approximations to the system of shallow water equations, part II: Discrete-time a priori error estimates

被引:17
作者
Chippada, S
Dawson, CN
Martinez-Canales, ML
Wheller, MF
机构
[1] Fluent Inc, Evanston, IL 60201 USA
[2] Univ Texas, Texas Inst Computat & Appl Math, Ctr Subsurface Modeling C0200, Austin, TX 78712 USA
[3] Stanford Univ, Dept Geol & Environm Sci, Stanford, CA 94305 USA
关键词
shallow water equations; surface flow; mass conservation; momentum conservation; finite element model; error estimate; stability;
D O I
10.1137/S0036142996314159
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Various sophisticated finite element models for surface water flow exist in the literature. Gray, Kolar, Luettich, Lynch, and Westerink have developed a hydrodynamic model based on the generalized wave continuity equation (GWCE) formulation and have formulated a Galerkin finite element procedure based on combining the GWCE with the nonconservative momentum equations. Numerical experiments suggest that this method is robust and accurate and suppresses spurious oscillations which plague other models. In this paper, we analyze a closely related Galerkin method which uses the conservative momentum equations (CME). For this GWCE-CME system of equations, we present, for discrete time, an a priori error estimate based on an L-2 projection.
引用
收藏
页码:226 / 250
页数:25
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