A space-time discontinuous Galerkin method for linear convection-dominated Sobolev equations

DOI10.1016/j.amc.2009.01.020zbMath1162.65390OpenAlexW2020284789MaRDI QIDQ1021549

Keying Ma, Tong-jun Sun

Publication date: 8 June 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.01.020

zbMATH Keywords

finite element methoddiscontinuous Galerkin methodspace-timeSobolev equationsRadau quadrature rule

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items

A hybrid high-order method for Sobolev equation with convection-dominated term ⋮ Analysis of a space-time continuous Galerkin method for convection-dominated Sobolev equations ⋮ A space-time spectral method for multi-dimensional Sobolev equations ⋮ Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations ⋮ A fully discrete discontinuous Galerkin method for nonlinear fractional Fokker-Planck equation ⋮ Treatment of fast moving loads in elastodynamic problems with a space-time variational formulation ⋮ Coupled problem of the inverse design and constraint optimization ⋮ Error analysis of a mixed finite element approximation of the semilinear Sobolev equations ⋮ Two-grid Methods for Finite Volume Element Approximations of Nonlinear Sobolev Equations ⋮ An expanded mixed covolume method for sobolev equation with convection term on triangular grids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations
• A coupled non-linear hyperbolic-Sobolev system
• Discontinuous Galerkin finite element methods for second order hyperbolic problems
• The finite difference streamline diffusion methods for Sobolev equations with convection-dominated term
• On a theory of heat conduction involving two temperature
• A quasilinear parabolic and a related third order problem
• Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]
• Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
• Time discretization of parabolic problems by the discontinuous Galerkin method
• Numerical Solution of Sobolev Partial Differential Equations
• Time-Stepping Galerkin Methods for Nonlinear Sobolev Partial Differential Equations
• A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
• Adaptive Finite Element Methods for Parabolic Problems II: Optimal Error Estimates in $L_\infty L_2 $ and $L_\infty L_\infty $
• Adaptive Finite Element Methods for Parabolic Problems IV: Nonlinear Problems
• Streamline-diffusion F. E. M. for Sobolev equations with convection-dominated term