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String gradient weighted moving finite elements
Author(s) -
Wacher Abigail,
Sobey Ian,
Miller Keith
Publication year - 2005
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.872
Subject(s) - discretization , mathematics , finite element method , partial differential equation , piecewise , string (physics) , mathematical analysis , manifold (fluid mechanics) , dimension (graph theory) , space (punctuation) , piecewise linear function , distribution (mathematics) , pure mathematics , physics , mathematical physics , computer science , mechanical engineering , engineering , thermodynamics , operating system
Moving finite element methods are well established for solution of systems of partial differential equations which contain regions where the solution is rapidly varying but moving. The string or second gradient weighted moving finite element method (SGWMFE) uses a piecewise linear discretization of a single evolving manifold to approximate the solution of the PDEs. In the case of one space dimension, x , and two dependent variables, u ( x , t ) and v ( x , t ), the solution is calculated from the normal motion of a single manifold [ x (τ, t ), u (τ, t ), v (τ, t )], where τ is a parameter along the maniflold, or a ‘string’ embedded in [ x , u , v ] space. This method can be extended to multiple dimensions and an arbitrary number of dependent variables in which case the ‘string’ parameterization analogy is replaced by a multi‐variable parameterization. In this paper, we outline the application of SGWMFE for solution of the shallow water equations in one and two space dimensions. We describe the results of a number of numerical experiments, including varying the initial distribution of nodes. Copyright © 2005 John Wiley & Sons, Ltd.