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SIAMNUM
2010
113views more  SIAMNUM 2010»
13 years 1 months ago
Compactness Properties of the DG and CG Time Stepping Schemes for Parabolic Equations
Abstract. It is shown that for a broad class of equations that numerical solutions computed using the discontinuous Galerkin or the continuous Galerkin time stepping schemes of arb...
Noel Walkington
SIAMNUM
2010
115views more  SIAMNUM 2010»
13 years 1 months ago
Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusi
In this paper, we study the superconvergence property for the discontinuous Galerkin (DG) and the local discontinuous Galerkin (LDG) methods, for solving one-dimensional time depe...
Yingda Cheng, Chi-Wang Shu
SIAMNUM
2010
114views more  SIAMNUM 2010»
13 years 1 months ago
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation
We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, finite volume, mix...
Alexandre Ern, Martin Vohralík
SIAMNUM
2010
118views more  SIAMNUM 2010»
13 years 1 months ago
Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities
Abstract. We study discontinuous Galerkin methods for solving elliptic variational inequalities, of both the first and second kinds. Analysis of numerous discontinuous Galerkin sch...
Fei Wang, Weimin Han, Xiao-Liang Cheng
JSCIC
2010
57views more  JSCIC 2010»
13 years 1 months ago
A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy
While second order methods for computational simulations of fluid flow provide the basis of widely used commercial software, there is a need for higher order methods for more accur...
Antony Jameson
SIAMSC
2011
105views more  SIAMSC 2011»
13 years 2 months ago
Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Improving Discontinuous Galerkin Solutions
Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering is a promising technique not only in improving the order of the numerical solution obtained by a disc...
Paulien van Slingerland, Jennifer K. Ryan, C. Vuik
SIAMNUM
2011
110views more  SIAMNUM 2011»
13 years 2 months ago
A Posteriori Error Control for Discontinuous Galerkin Methods for Parabolic Problems
We derive energy-norm a posteriori error bounds for an Euler timestepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For acc...
Emmanuil H. Georgoulis, Omar Lakkis, Juha M. Virta...
MOC
2011
13 years 2 months ago
Convergence of a mixed method for a semi-stationary compressible Stokes system
We propose and analyze a finite element method for a semi– stationary Stokes system modeling compressible fluid flow subject to a Navier– slip boundary condition. The veloci...
Kenneth H. Karlsen, Trygve K. Karper
SIAMSC
2010
157views more  SIAMSC 2010»
13 years 5 months ago
Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
We propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the ha...
Yanlai Chen, Jan S. Hesthaven, Yvon Maday, Jer&oac...
MOC
2002
127views more  MOC 2002»
13 years 6 months ago
The dynamical behavior of the discontinuous Galerkin method and related difference schemes
We study the dynamical behavior of the discontinuous Galerkin finite element method for initial value problems in ordinary differential equations. We make two different assumptions...
Donald J. Estep, Andrew M. Stuart