Discrepancy between theory and real computation on the stability of some finite element schemes

DOI10.1016/j.cam.2005.08.042zbMath1108.65092OpenAlexW2129925087MaRDI QIDQ861923

Masahisa Tabata

Publication date: 2 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.cam.2005.08.042

zbMATH Keywords

stabilityinstabilityfinite element methodconvection-diffusion equationnumerical examplesmethod of characteristics

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) 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 exactly computable Lagrange–Galerkin scheme for the Navier–Stokes equations and its error estimates ⋮ A single-step characteristic-curve finite element scheme of second order in time for the incompressible Navier-Stokes equations ⋮ Stabilized Lagrange–Galerkin Schemes of First- and Second-Order in Time for the Navier–Stokes Equations ⋮ Error estimates of a stabilized Lagrange−Galerkin scheme for the Navier−Stokes equations ⋮ Conditional stability of the Lagrange-Galerkin scheme with numerical quadrature ⋮ Second-Order Finite Difference Approximations of the Upper-Convected Time Derivative ⋮ A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems

Cites Work

• Unnamed Item
• A second order characteristic finite element scheme for convection-diffusion problems
• An upwind finite element scheme for high-Reynolds-number flows

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