Journal ArticleDOI
Finite element solution of time-dependent problems
D. J. Evans,A. A. Al-kharafi +1 more
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In this article, the authors compare the finite element solution of some illustrative time-dependent problems involving parabolic and hyperbolic partial differential equations with alternative solution methods, and show that finite element solutions are not the best solution methods for these problems.Abstract:
In this paper the authors compare the finite element solution of some illustrative time-dependent problems involving parabolic and hyperbolic partial differential equations with alternative solution methods.read more
Citations
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Journal ArticleDOI
High-order local absorbing conditions for the wave equation: Extensions and improvements
TL;DR: A formulation of local high-order ABCs recently proposed by Hagstrom and Warburton and based on a modification of the Higdon ABCs, is further developed and extended in a number of ways.
Journal ArticleDOI
High-order Absorbing Boundary Conditions for anisotropic and convective wave equations
TL;DR: High-order Absorbing Boundary Conditions (ABCs), applied on a rectangular artificial computational boundary that truncates an unbounded domain, are constructed for a general two-dimensional linear scalar time-dependent wave equation which represents acoustic wave propagation in anisotropic and subsonically convective media.
Journal ArticleDOI
A Spectral Element Solution of the Klein-Gordon Equation with High-Order Treatment of Time and Non-Reflecting Boundary
TL;DR: In this paper, a spectral element (SE) implementation of the Givoli-Neta non-reflecting boundary condition (NRBC) is considered for the solution of the Klein-Gordon equation.
Journal ArticleDOI
Double absorbing boundary formulations for acoustics and elastodynamics
TL;DR: The energy method is employed to obtain uniform-in-time estimates of the norm of the solution and the auxiliary functions, thus establishing the well-posedness and asymptotic stability of the DAB formulation.
ReportDOI
A Study of Lateral Boundary Conditions for the NRL's Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS)
Beny Neta,Dan Givoli +1 more
TL;DR: In this paper, the authors developed high order non-reflecting boundary conditions for the dispersive Klein-Gordon equation and the linearized shallow water equations for a limited-area model, where lateral edges are not physical boundaries of flow but constitute artificial constraints imposed by computational considerations.
References
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Book
Finite Element Analysis and Applications
R. Wait,Andrew R. Mitchell +1 more
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-dependency-heavy and therefore expensive process of approximating discrete-time approximation.
Journal ArticleDOI
A finite element approach to Burgers' equation
J. Caldwell,P. Wanless,A.E. Cook +2 more
TL;DR: In this article, a piecewise polynomial approximation of Burgers' equation is proposed, where the size of the elements is chosen to take into account the nature of the solution.
Journal ArticleDOI
The Group Explicit method for the solution of Burger's equation
TL;DR: The aim of this paper is to extend the application of the Group Explicit method to the numerical solution of a non-linear parabolic partial differential equation of second order to show that the method is accurate and comparable to existing finite difference methods.
Journal ArticleDOI
The finite element solution of a quasi-linear elliptic equation governing non-Newtonian flows through rectangular ducts
A. A. Al-Kharafi,D.J. Evans +1 more
TL;DR: A Rayleigh-Ritz finite element method (FEM) using quadratic, cubic and quartic elements has been used to solve the steady laminar flow of a non-Newtonian fluid through rectangular ducts as discussed by the authors.
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