A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

DOI10.1007/BF01385737zbMath0791.65070OpenAlexW2020674455MaRDI QIDQ1326390

V. Pereyra

Publication date: 18 May 1994

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133720

zbMATH Keywords

finite elementmethod of linesa posteriori error estimationlinear initial-boundary value problemslocal parabolic

Mathematics Subject Classification ID

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (30)

Parallel, adaptive finite element methods for conservation laws ⋮ A comparison of adaptive software for 1D parabolic PDEs ⋮ Adaptive \(s\)-method for linear elastostatics ⋮ A Posteriori Finite Element Error Analysis for Symmetric Positive Differential Equations ⋮ A posteriori error estimates for parabolic differential systems solved by the finite element method of lines ⋮ A POSTERIORIERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS ⋮ Integrated space-time adaptive \(hp\)-refinement methods for parabolic systems ⋮ A COMPLETE ANALYSIS FOR SOMEA POSTERIORIERROR ESTIMATES WITH THE FINITE ELEMENT METHOD OF LINES FOR A NONLINEAR PARABOLIC EQUATION ⋮ A posteriori error estimation for the method of lumped masses applied to second-order hyperbolic problems ⋮ Fully discrete error estimation by the method of lines for a nonlinear parabolic problem. ⋮ An implicit interpolation error-based error estimation strategy for hp-adaptivity in one space dimension ⋮ A high-order global spatially adaptive collocation method for 1-D parabolic PDEs ⋮ Grid adjustment for parabolic systems based on a posteriori error estimates ⋮ A posteriori error estimates for optimal distributed control governed by the evolution equations ⋮ Interpolation error-based a posteriori error estimation for \(hp\)-refinement using first and second derivative jumps. ⋮ Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions. ⋮ Comparison of hp-adaptive error estimates for second order hyperbolic systems ⋮ A sparse grid space-time discretization scheme for parabolic problems ⋮ High-order adaptive finite element-singly implicit Runge-Kutta methods for parabolic differential equations ⋮ Exact a posteriori error analysis of the least squares finite element method ⋮ Error estimates and adaptive finite element methods ⋮ A posteriori error estimation and adaptivity in the method of lines with mixed finite elements. ⋮ Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem ⋮ Prediction and the quantification of uncertainty ⋮ A posteriori boundary element error estimation ⋮ Even-odd goal-oriented a posteriori error estimation for elliptic problems ⋮ Parallel computation with adaptive methods for elliptic and hyperbolic systems ⋮ A posteriori error estimates for fourth-order elliptic problems ⋮ A posteriori finite element error estimation for second-order hyperbolic problems. ⋮ Grid adjustment based on a posteriori error estimators

Uses Software

• DASSL

Cites Work

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• Error Estimates for Adaptive Finite Element Computations
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