Space-time discretization of the heat equation

DOI10.1007/s11075-013-9818-4zbMath1304.65216arXiv1212.6037OpenAlexW1596622131MaRDI QIDQ478187

Roman Andreev

Publication date: 3 December 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6037

zbMATH Keywords

heat equationnumerical examplespreconditioningfinite elementparallel computationimplementation\texttt{Matlab}linear parabolic evolution equationsPetrov-Galerkin discretizationspace-time discretization

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Parallel numerical computation (65Y05) Preconditioners for iterative methods (65F08)

Related Items (12)

Space-time \(hp\)-approximation of parabolic equations ⋮ A well-conditioned direct pint algorithm for first- and second-order evolutionary equations ⋮ Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations ⋮ Error analysis for discretizations of parabolic problems using continuous finite elements in time and mixed finite elements in space ⋮ Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs ⋮ Optimization problems for PDEs in weak space-time form. Abstracts from the workshop held March 5--10, 2023 ⋮ A finite addition of matter elements method for modeling and solution of an SLM thermal problem by a multiscale method ⋮ An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems ⋮ Space-time least-squares finite elements for parabolic equations ⋮ Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods ⋮ On long time integration of the heat equation ⋮ Fractional Space-Time Variational Formulations of (Navier--) Stokes Equations

Uses Software

• LSQR
• Matlab
• spacetime
• na14
• CRAIG

Cites Work

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• Space-time adaptive wavelet methods for parabolic evolution problems
• The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
• Stopping Criteria for the Iterative Solution of Linear Least Squares Problems
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Solving Generalized Least-Squares Problems with LSQR
• A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature
• Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
• The h‐p version of the finite element method for parabolic equations. II. The h‐p version in time
• One-Step Piecewise Polynomial Galerkin Methods for Initial Value Problems

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