Local projection stabilisation for higher order discretisations of convection-diffusion problems on Shishkin meshes

DOI10.1007/s10444-008-9070-yzbMath1165.65064OpenAlexW1996257128MaRDI QIDQ1016134

Gunar Matthies

Publication date: 4 May 2009

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-008-9070-y

zbMATH Keywords

stabilizationconvection-diffusion equationShishkin meshConvection-diffusion problemsquadrilateral finite elementslocal projection methodexponential bounday layers

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (9)

Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012 ⋮ Superconvergence using pointwise interpolation in convection-diffusion problems ⋮ A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time ⋮ Robust error estimation in energy and balanced norms for singularly perturbed fourth order problems ⋮ Local projection stabilisation on \(S\)-type meshes for convection-diffusion problems with characteristic layers ⋮ Local projection methods on layer-adapted meshes for higher order discretisations of convection-diffusion problems ⋮ Convergence on layer-adapted meshes and anisotropic interpolation error estimates of non-standard higher order finite elements ⋮ Supercloseness of continuous interior penalty methods on Shishkin triangular meshes and hybrid meshes for singularly perturbed problems with characteristic layers ⋮ Higher order uniformly convergent NIPG methods for 1-d singularly perturbed problems of convection-diffusion type

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