A fully-discrete local discontinuous Galerkin method for convection-dominated Sobolev equation

DOI10.1007/s10915-011-9498-yzbMath1244.65145OpenAlexW2066783603MaRDI QIDQ427210

Fuzheng Gao, Qiang Zhang

Publication date: 13 June 2012

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-011-9498-y

zbMATH Keywords

Cauchy problemerror estimatelocal discontinuous Galerkin methodnonlinear Sobolev equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (32)

Error analysis of the semi-discrete local discontinuous Galerkin method for compressible miscible displacement problem in porous media ⋮ Unnamed Item ⋮ A Weak Galerkin Mixed Finite Element Method for Acoustic Wave Equation ⋮ Stability analysis and error estimates of implicit-explicit Runge-Kutta local discontinuous Galerkin methods for nonlinear fractional convection-diffusion problems ⋮ Optimal energy conserving and energy dissipative local discontinuous Galerkin methods for the Benjamin-Bona-Mahony equation ⋮ Stability analysis and error estimates of implicit Runge-Kutta local discontinuous Galerkin methods for linear bi-harmonic equation ⋮ On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation ⋮ Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit backward difference formulas up to fifth order for convection-diffusion equation ⋮ Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation ⋮ Uniform stability for local discontinuous Galerkin methods with implicit-explicit Runge-Kutta time discretizations for linear convection-diffusion equation ⋮ Analysis of the Implicit-Explicit Ultra-Weak Discontinuous Galerkin Method for Convection-Diffusion Problems ⋮ Numerical solutions of two dimensional Sobolev and generalized Benjamin-Bona-Mahony-Burgers equations via Haar wavelets ⋮ A new projection-based stabilized virtual element method for the Stokes problem ⋮ Linearized compact difference methods combined with Richardson extrapolation for nonlinear delay Sobolev equations ⋮ Numerical simulation of the modified regularized long wave equation by split least-squares mixed finite element method ⋮ A combined mixed finite element method and local discontinuous Galerkin method for miscible displacement problem in porous media ⋮ Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems ⋮ Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation ⋮ B-spline quasi-interpolation based numerical methods for some Sobolev type equations ⋮ Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Time-Fractional Kdv Equation ⋮ Weak Galerkin finite element methods for Sobolev equation ⋮ Local discontinuous Galerkin methods with generalized alternating numerical fluxes for two-dimensional linear Sobolev equation ⋮ Meshless RBFs method for numerical solutions of two-dimensional high order fractional Sobolev equations ⋮ \(L^2\)-stability analysis of IMEX-\(( \sigma,\mu )\) DG schemes for linear advection-diffusion equations ⋮ A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation ⋮ Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems ⋮ Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems ⋮ Strong Stability of Explicit Runge--Kutta Time Discretizations ⋮ Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order ⋮ Enforcing strong stability of explicit Runge-Kutta methods with superviscosity ⋮ Application of meshfree spectral method for the solution of multi-dimensional time-fractional Sobolev equations ⋮ Analysis of new conservative difference scheme for two-dimensional Rosenau-RLW equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation
• The convergence of fully discrete Galerkin approximations for the Benjamin--Bona--Mahony (BBM) equation
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Error estimates for a Galerkin method for a class of model equations for long waves
• Application of a lumped Galerkin method to the regularized long wave equation
• \(H^1\)-Galerkin mixed finite element method for the regularized long wave equation
• A Petrov-Galerkin finite element scheme for the regularized long wave equation
• Numerical solution of regularized long wave equation using Petrov-Galerkin method
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• A Local Discontinuous Galerkin Method for the Camassa–Holm Equation
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• Riemann Solvers, the Entropy Condition, and Difference
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Time-Stepping Galerkin Methods for Nonlinear Sobolev Partial Differential Equations
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations
• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• A Local Discontinuous Galerkin Method for KdV Type Equations
• Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws

This page was built for publication: A fully-discrete local discontinuous Galerkin method for convection-dominated Sobolev equation