A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

DOI10.1090/S0025-5718-2014-02912-8zbMath1310.65127arXiv0709.0916MaRDI QIDQ5246832

Omar Lakkis, Tristan Pryer, Charalambos G. Makridakis

Publication date: 22 April 2015

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

Full work available at URL: https://arxiv.org/abs/0709.0916

zbMATH Keywords

convergenceheat equationdissipationdualityoptimalityfinite element methodssuperconvergencereaction-diffusiona posteriori error estimateelliptic reconstructionlinear parabolic PDE

Mathematics Subject Classification ID

Adaptive control/observation systems (93C40) 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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer (80M10)

Related Items (5)

Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems ⋮ A priori and a posteriori error estimates of the weak Galerkin finite element method for parabolic problems ⋮ A Posteriori Error Estimation and Adaptivity for Nonlinear Parabolic Equations using IMEX-Galerkin Discretization of Primal and Dual Equations ⋮ Conservative Galerkin methods for dispersive Hamiltonian problems ⋮ Delay-dependent elliptic reconstruction and optimal 𝐿^{∞}(𝐿²) a posteriori error estimates for fully discrete delay parabolic problems

Uses Software

• ALBERTA

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