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Higher-order finite element methods.
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This article is published in Mathematics of Computation.The article was published on 2005-01-01 and is currently open access. It has received 190 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.read more
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Journal ArticleDOI
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
TL;DR: F Fourier analysis of the two-level p-multigrid algorithm for convection-diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids.
Journal ArticleDOI
Algorithms and data structures for massively parallel generic adaptive finite element codes
TL;DR: This work develops scalable algorithms and data structures for generic finite element methods that consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing, and removes the bottlenecks that typically limit large-scale adaptive finite element analyses.
A set of symmetric quadrature rules on triangles and tetrahedra
Linbo Zhang,Tao Cui,Hui Liu +2 more
TL;DR: A program for computing symmetric quadrature rules on triangles and tetrahedra is presented and a set of rules are obtained which are useful for use in finite element computations.
Journal ArticleDOI
Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
Xiaobing Feng,Haijun Wu +1 more
TL;DR: This paper develops and analyzes some interior penalty discontinuous Galerkin (IPDG) methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in two and three dimensions and proves that they are stable and well-posed.
Journal ArticleDOI
An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations
Ralf Hartmann,Paul Houston +1 more
TL;DR: A new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations is proposed, showing the optimality of the proposed method when the error is measured in terms of both the L"2-norm and for certain target functionals.
References
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Journal ArticleDOI
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
TL;DR: F Fourier analysis of the two-level p-multigrid algorithm for convection-diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids.
Journal ArticleDOI
Algorithms and data structures for massively parallel generic adaptive finite element codes
TL;DR: This work develops scalable algorithms and data structures for generic finite element methods that consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing, and removes the bottlenecks that typically limit large-scale adaptive finite element analyses.
A set of symmetric quadrature rules on triangles and tetrahedra
Linbo Zhang,Tao Cui,Hui Liu +2 more
TL;DR: A program for computing symmetric quadrature rules on triangles and tetrahedra is presented and a set of rules are obtained which are useful for use in finite element computations.
Journal ArticleDOI
Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
Xiaobing Feng,Haijun Wu +1 more
TL;DR: This paper develops and analyzes some interior penalty discontinuous Galerkin (IPDG) methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in two and three dimensions and proves that they are stable and well-posed.
Journal ArticleDOI
An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations
Ralf Hartmann,Paul Houston +1 more
TL;DR: A new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations is proposed, showing the optimality of the proposed method when the error is measured in terms of both the L"2-norm and for certain target functionals.