Space-time \(hp\)-approximation of parabolic equations

DOI10.1007/s10092-018-0275-2zbMath1404.65118OpenAlexW2885919413MaRDI QIDQ1616098

Denis Devaud, Christoph Schwab

Publication date: 31 October 2018

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-018-0275-2

zbMATH Keywords

exponential convergenceparabolic differential equationsspace-time discretization\(hp\)-approximation

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)

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A Parallel Algorithm for Solving Linear Parabolic Evolution Equations, Adaptive space-time finite element methods for non-autonomous parabolic problems with distributional sources, Space-Time Finite Element Methods for Parabolic Initial-Boundary Value Problems with Non-smooth Solutions, Coercive space-time finite element methods for initial boundary value problems, Space-time least-squares finite elements for parabolic equations, An exact realization of a modified Hilbert transformation for space-time methods for parabolic evolution equations, Further results on a space-time FOSLS formulation of parabolic PDEs, Adaptive space-time finite element methods for parabolic optimal control problems

Cites Work

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• Space-time discretization of the heat equation
• Space-time finite element methods for parabolic problems
• Numerical solution of parabolic problems based on a weak space-time formulation
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• An \(hp\) a priori error analysis of the DG time-stepping for initial value problems
• Theory and practice of finite elements.
• Space-time isogeometric analysis of parabolic evolution problems
• Stability of Petrov-Galerkin discretizations: application to the space-time weak formulation for parabolic evolution problems
• 50 Years of Time Parallel Time Integration
• Analysis in Banach Spaces
• Space-time adaptive wavelet methods for parabolic evolution problems
• Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems
• Convergence rates for adaptive finite elements
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
• Fractional Space-Time Variational Formulations of (Navier--) Stokes Equations
• Finite Elemente
• Galerkin Finite Element Methods for Parabolic Problems
• \(hp\)-discontinuous Galerkin time stepping for parabolic problems