A uniform optimal‐order estimate for an Eulerian‐Lagrangian discontinuous Galerkin method for transient advection–diffusion equations

DOI10.1002/num.20338zbMath1166.65047OpenAlexW2166868267MaRDI QIDQ5503306

Kaixin Wang

Publication date: 13 January 2009

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20338

zbMATH Keywords

discontinuous Galerkin methoderror estimateboundary layersadvection-diffusion equationscharacteristic methodsEulerian-Lagrangian methodinterior penalty methods

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15)

Related Items (7)

An optimal-order error estimate for a Galerkin-mixed finite-element time-stepping procedure for porous media flows ⋮ An Eulerian-Lagrangian control volume scheme for two-dimensional unsteady advection-diffusion problems ⋮ Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Semi-Lagrangian formulation for the advection-diffusion-absorption equation ⋮ A single-node characteristic collocation method for unsteady-state convection-diffusion equations in three-dimensional spaces ⋮ A characteristics-mixed covolume method for a convection-dominated transport problem

Cites Work

• A discontinuous \(hp\) finite element method for diffusion problems
• The modified method of characteristics with adjusted advection
• Uniform Estimates for Eulerian–Lagrangian Methods for Singularly Perturbed Time-Dependent Problems
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Eulerian-Lagrangian localized adjoint methods for convection-diffusion equations and their convergence analysis

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