Convergence of a step-doubling Galerkin method for parabolic problems

DOI10.1090/S0025-5718-04-01696-5zbMath1072.65120MaRDI QIDQ4671828

Todd F. Dupont, Bruce P. Ayati

Publication date: 27 April 2005

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

stabilityGalerkin methodfinite element methodconvection-diffusion equationimplicit Euler methodRichardson extrapolationa posteriori error boundtime-step control

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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A structured-population model of Proteus mirabilis swarm-colony development ⋮ The explicit-implicit-null method: removing the numerical instability of PDEs ⋮ Modeling the role of the cell cycle in regulating Proteus mirabilis swarm-colony development ⋮ Convergence of a step-doubling Galerkin method for parabolic problems ⋮ A comparison of the dynamics of the structured cell population in virtual and experimental Proteus mirabilis swarm colonies ⋮ MARS: a method for the adaptive removal of stiffness in PDEs

Cites Work

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• Local error estimation by doubling
• Evaporative instabilities in climbing films
• Nonlinear dynamics and breakup of free-surface flows
• Axial instability of a free-surface front in a partially filled horizontal rotating cylinder
• Efficient Higher Order Single Step Methods for Parabolic Problems: Part I
• Drop formation in a one-dimensional approximation of the Navier–Stokes equation
• Convergence of a step-doubling Galerkin method for parabolic problems
• A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations

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