Parallel, adaptive finite element methods for conservation laws
type: Item
instance of: scholarly article
title: Parallel, adaptive finite element methods for conservation laws
zbMATH Open document ID: 0826.65084
DOI: 10.1016/0168-9274(94)90029-9
author: Rupak Biswas
author: Karen D. Devine
author: J. E. Flaherty
published in: Applied Numerical Mathematics
publication date: 1995-12-04T00:00:00Z
review text: The authors explore extensively how to numerically solve hyperbolic conservation laws by means of nonconforming finite elements; computations are to be carried on parallel computers and a significant set of examples in one and two dimensions is analyzed, with an explicit Runge-Kutta method being employed for time discretization. In this way, discontinuities that may develop with time in hyperbolic phenomena are implicit in the discretization from the onset. Adaptive \(h\)- and \(p\)- refinements are shown to provide accuracy at low computational cost, when compared with fixed meshes computations. The paper sets the lines for further developments combining both types of refinement, in order ``to optimize computational work in both smooth and discontinuous solution regions'' (sic).
reviewed by: Juan Pedro Milaszewicz
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 609622
zbMATH Keywords: \(h\)-refinements
zbMATH Keywords: hyperbolic conservation laws
zbMATH Keywords: nonconforming finite elements
zbMATH Keywords: parallel computers
zbMATH Keywords: explicit Runge-Kutta method
zbMATH Keywords: time discretization
zbMATH Keywords: \(p\)-refinements
zbMATH Keywords: discontinuous solution
MaRDI profile type: Publication
full work available at URL: 0168-9274(94)90029-9
OpenAlex ID: W2038107889
cites work: High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems
cites work: Second-order finite element approximations and a posteriori error estimation for two-dimensional parabolic systems
cites work: High-order adaptive methods for parabolic systems
cites work: A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems
cites work: An adaptive local mesh refinement method for time-dependent partial differential equations
cites work: Q3817903
cites work: Robust, geometrically based, automatic two‐dimensional mesh generation
cites work: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
cites work: The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
cites work: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
cites work: TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
cites work: A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics
cites work: High order filtering methods for approximating hyperbolic systems of conservation laws
cites work: An expert system for the optimal mesh design in thehp-version of the finite element method
cites work: Q5536978
cites work: Approximate Riemann solvers, parameter vectors, and difference schemes
cites work: Total-Variation-Diminishing Time Discretizations
cites work: TVB Boundary Treatment for Numerical Solutions of Conservation Laws
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
cites work: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
cites work: High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
cites work: Towards the ultimate conservative difference scheme. IV: A new approach to numerical convection
description: scientific article; zbMATH DE number 609622