Journal ArticleDOI
The Taylor-Galerkin discontinuous finite element method—An explicit scheme for nonlinear hyperbolic conservation laws
Kyu Y. Choe,Keith A. Holsapple +1 more
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TLDR
In this article, a two-dimensional Taylor-Galerkin discontinuous finite element method for the computation of weak solutions of nonlinear hyperbolic conservation laws is presented, and the resulting scheme is explicit and solves the problem element by element.About:
This article is published in Finite Elements in Analysis and Design.The article was published on 1991-12-01. It has received 6 citations till now. The article focuses on the topics: Discontinuous Galerkin method & Mixed finite element method.read more
Citations
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The discontinuous Galerkin method with Lax–Wendroff type time discretizations
TL;DR: A Lax–Wendroff time discretization procedure for the discontinuous Galerkin method (LWDG) to solve hyperbolic conservation laws is developed and is more cost effective than the Runge–KuttaTime discretizations for certain problems including two-dimensional Euler systems of compressible gas dynamics when nonlinear limiters are applied.
Journal ArticleDOI
3D unstructured mesh ALE hydrodynamics with the upwind discontinuous finite element method
TL;DR: A numerical scheme to solve 3D Arbitrary Lagrangian-Eulerian (ALE) hydrodynamics on an unstructured mesh using discontinuous finite element space and an explicit Runge-Kutta time discretization that has second-order accuracy in smooth regions appears to be robust.
On the numerical simulation of the multilayer injection moulding process
TL;DR: A submitted manuscript is the version of the article upon submission and before peer-review as mentioned in this paper, while a published version is the final layout of the paper including the volume, issue and page numbers.
Journal ArticleDOI
The discontinuous finite element method with the Taylor-Galerkin approach for nonlinear hyperbolic conservation laws
Kyu Y. Choe,Keith A. Holsapple +1 more
TL;DR: In this paper, a one-step, explicit finite element scheme was developed for the computation of weak solutions of nonlinear hyperbolic conservation laws in one dimension, which is an improved version of the discontinuous finite element method using the Taylor-Galerkin procedure.
Journal ArticleDOI
The high order control volume discontinuous Petrov-Galerkin finite element method for the hyperbolic conservation laws based on Lax-Wendroff time discretization
Guozhong Zhao,Xijun Yu +1 more
TL;DR: A high order control volume discontinuous finite element method for both scalar and systems of hyperbolic conservation laws based on Lax-Wendroff time discretization that can preserve local conservation.
References
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Finite difference methods for numerical computation of discontinous solutions of the equations of fluid dynamics
Journal ArticleDOI
Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
TL;DR: In this paper, an approach to numerical convection is presented that exclusively yields upstream-centered schemes, which start from a meshwise approximation of the initial-value distribution by simple basic functions, e.g., Legendre polynomials.
Journal ArticleDOI
TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: In this paper, a classe de methodes a elements finis de Galerkin discontinues a variation totale bornee for the resolution des lois de conservation, and the convergence of the convergence is studied.
Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics
S. K. Godunov,I. Bohachevsky +1 more
TL;DR: In this paper, the authors proposed a method of characteristics used for numerical computation of solutions of fluid dynamical equations is characterized by a large degree of non standardness and therefore is not suitable for automatic computation on electronic computing machines, especially for problems with a large number of shock waves and contact discontinuities.
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