Strong and weak Lagrange-Galerkin spectral element methods for the shallow water equations
نویسندگان
چکیده
منابع مشابه
Strong and weak Lagrange-Galerkin spectral element methods for the shallow water equations
The Lagrange-Galerkin spectral element method for the two-dimensional shallow water equations is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the nonlinearities introduced by the advection operator o...
متن کاملEuler–Lagrange equations for the spectral element shallow water system
We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with...
متن کاملHigh-order discontinuous element-based schemes for the inviscid shallow water equations: Spectral multidomain penalty and discontinuous Galerkin methods
Two commonly used types of high-order-accuracy element-based schemes, collocationbased spectral multidomain penalty methods (SMPM) and nodal discontinuous Galerkin methods (DGM), are compared in the framework of the inviscid shallow water equations. Differences and similarities in formulation are identified, with the primary difference being the dissipative term in the Rusanov form of the numer...
متن کاملHybridized Discontinuous Galerkin Methods for Linearized Shallow Water Equations
We present a systematic and constructive methodology to devise various hybridized discontinuous Galerkin (HDG) methods for linearized shallow water equations. At the heart of our development is an upwind HDG framework obtained by hybridizing the upwind flux in the standard discontinuous Galerkin (DG) approach. The chief idea is to first break the uniqueness of the upwind flux across element bou...
متن کاملThe Lagrange-Galerkin Method for the Two-dimensional Shallow Water Equations on Adaptive Grids
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2003
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(03)80010-x