Interior penalty discontinuous Galerkin methods with implicit time-integration techniques for nonlinear parabolic equations

DOI10.1002/num.21758zbMath1281.65131OpenAlexW2074590724MaRDI QIDQ2846185

Gung-Min Gie, Ming-Cheng Shiue, Lun-Ji Song

Publication date: 5 September 2013

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

Full work available at URL: https://doi.org/10.1002/num.21758

zbMATH Keywords

numerical resultsnonlinear parabolic equationexistenceporous mediumdiscontinuous Galerkin methoderror estimatesemidiscretizationnumerical stabilityinterior penalty

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Flows in porous media; filtration; seepage (76S05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations ⋮ Symmetric interior penalty Galerkin approaches for two-dimensional parabolic interface problems with low regularity solutions ⋮ Analysis of a full-discrete two-grid discontinuous Galerkin method for nonlinear parabolic equations ⋮ A two‐grid discontinuous Galerkin method for an incompressible miscible displacement problem ⋮ A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation ⋮ A two-grid discontinuous Galerkin method for a kind of nonlinear parabolic problems ⋮ Error analysis of a two-grid discontinuous Galerkin method for non-linear parabolic equations ⋮ A two-grid combined mixed finite element and discontinuous Galerkin method for an incompressible miscible displacement problem in porous media ⋮ Uniqueness of numerical solutions to nonlinear parabolic equations by a fully implicit discontinuous Galerkin method

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