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Continuous, discontinuous and coupled discontinuous–continuous Galerkin finite element methods for the shallow water equations
Author(s) -
Dawson Clint,
Westerink Joannes J.,
Feyen Jesse C.,
Pothina Dharhas
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1156
Subject(s) - discontinuous galerkin method , finite element method , galerkin method , shallow water equations , mathematics , coupling (piping) , momentum (technical analysis) , mathematical analysis , advection , enhanced data rates for gsm evolution , computer science , physics , engineering , structural engineering , mechanical engineering , finance , economics , thermodynamics , telecommunications
We consider the approximation of the depth‐averaged two‐dimensional shallow water equations by both a traditional continuous Galerkin (CG) finite element method as well as two discontinuous Galerkin (DG) approaches. The DG method is locally conservative, flux‐continuous on each element edge, and is suitable for both smooth and highly advective flows. A novel technique of coupling a DG method for continuity with a CG method for momentum is developed. This formulation is described in detail and validation via numerical testing is presented. Comparisons between a widely used CG approach, a conventional DG method, and the novel coupled discontinuous–continuous Galerkin method illustrates advantages and disadvantages in accuracy and efficiency. Copyright © 2006 John Wiley & Sons, Ltd.