Finite Element Approximations to the System of Shallow Water Equations, Part I: Continuous Time a Priori Error Estimates

Chippada, S.Dawson, Clint N.Martinez, M.L.Wheeler, Mary F.2018-06-182018-06-181995-12Chippada, S., Dawson, Clint N., Martinez, M.L., et al.. "Finite Element Approximations to the System of Shallow Water Equations, Part I: Continuous Time a Priori Error Estimates." (1995) <a href="https://hdl.handle.net/1911/101873">https://hdl.handle.net/1911/101873</a>.https://hdl.handle.net/1911/101873Various 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, accurate and suppresses spurious oscillations which plague other models. We analyze a slightly modified Galerkin model which uses the conservative momentum equations (CME). For this GWCE-CME system of equations, we present an a priori error estimate based on an L² projection.26 ppengFinite Element Approximations to the System of Shallow Water Equations, Part I: Continuous Time a Priori Error EstimatesTechnical reportTR95-35