On a posteriori error control for the Allen-Cahn problem

DOI10.1002/mma.2894zbMath1281.65120OpenAlexW2152498898MaRDI QIDQ2870722

Emmanuil H. Georgoulis, Charalambos G. Makridakis

Publication date: 21 January 2014

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2894

zbMATH Keywords

finite element methoda posteriori error estimationphase fieldAllen-Cahn problem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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)

Related Items (9)

Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems ⋮ Recovery type a posteriori error estimation of an adaptive finite element method for Cahn-Hilliard equation ⋮ An adaptive variational procedure for the conservative and positivity preserving Allen-Cahn phase-field model ⋮ Numerically computable a posteriori-bounds for the stochastic Allen-Cahn Equation ⋮ A posteriori error bounds for fully-discrete \textit{hp}-discontinuous Galerkin timestepping methods for parabolic problems ⋮ Pointwise a Posteriori Error Bounds for Blow-Up in the Semilinear Heat Equation ⋮ A Posteriori Error Estimates for the Allen--Cahn Problem ⋮ Stability analysis and best approximation error estimates of discontinuous time-stepping schemes for the Allen–Cahn equation ⋮ Conditional A Posteriori Error Bounds for High Order Discontinuous Galerkin Time Stepping Approximations of Semilinear Heat Models with Blow-up

Cites Work

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• Maximum Norm Error Estimators for Three-Dimensional Elliptic Problems
• A posteriorierror control for the Allen–Cahn problem: circumventing Gronwall's inequality

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