Journal ArticleDOI
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Ralf Hartmann,Paul Houston +1 more
TLDR
An approach for the design of adaptive discontinuous Galerkin finite element methods is applied to physically relevant problems arising in inviscid compressible fluid flows governed by the Euler equations of gas dynamics, providing reliable and efficient error estimation.About:
This article is published in Journal of Computational Physics.The article was published on 2002-12-10. It has received 402 citations till now. The article focuses on the topics: Discontinuous Galerkin method & Mixed finite element method.read more
Citations
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Journal ArticleDOI
deal.II—A general-purpose object-oriented finite element library
TL;DR: The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools.
Journal ArticleDOI
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics
TL;DR: Recent adaptive results from a variety of laminar and Reynolds-averaged Navier-Stokes applications show the power of output-based adaptive methods for improving the robustness of computational fluid dynamics computations, however, challenges and areas of additional future research remain.
Journal ArticleDOI
Limiters for high-order discontinuous Galerkin methods
TL;DR: A limiter for the discontinuous Galerkin method is described that retains as high an order as possible, and does not automatically reduce to first order, and is extended to two-dimensional problems on tensor-product meshes.
Journal ArticleDOI
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
TL;DR: A novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell resolution properties of the DG method.
Journal ArticleDOI
A triangular cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations
TL;DR: Robustness of the cut-cell and adaptation technique is successfully tested for highly anisotropic boundary-layer meshes representative of practical high Re simulations, and results show that, for all test cases considered, p=2 and p=3 discretizations meet desired error tolerances using fewer degrees of freedom than p=1.
References
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Book
Finite Element Analysis
B. A. Szabó,Ivo Babuška +1 more
TL;DR: In this article, the authors present a general solution based on the principle of virtual work for two-dimensional linear elasticity problems and their convergence rates in one-dimensional dimensions. But they do not consider the case of three-dimensional LEL problems.
Book
A Posteriori Error Estimation in Finite Element Analysis
Mark Ainsworth,J. Tinsley Oden +1 more
TL;DR: In this paper, a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics is presented, focusing on methods for linear elliptic boundary value problems.
Book
A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques
TL;DR: Introduction.
Journal ArticleDOI
An optimal control approach to a posteriori error estimation in finite element methods
Roland Becker,Rolf Rannacher +1 more
TL;DR: The ‘dual-weighted-residual method’ is introduced initially within an abstract functional analytic setting, and is then developed in detail for several model situations featuring the characteristic properties of elliptic, parabolic and hyperbolic problems.
Book ChapterDOI
The Development of Discontinuous Galerkin Methods
TL;DR: An overview of the evolution of the discontinuous Galerkin methods since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until their most recent developments is presented.
Related Papers (5)
An optimal control approach to a posteriori error estimation in finite element methods
Roland Becker,Rolf Rannacher +1 more
A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations
Francesco Bassi,Stefano Rebay +1 more