Further results on a space-time FOSLS formulation of parabolic PDEs

DOI10.1051/m2an/2020084zbMath1470.35171arXiv2005.11000OpenAlexW3026107598WikidataQ114105440 ScholiaQ114105440MaRDI QIDQ5006307

Gregor Gantner, Rob P. Stevenson

Publication date: 13 August 2021

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.11000

zbMATH Keywords

convergence of adaptive algorithmFirst-Order System Least-Squares formulationspace-time FOSLS

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Initial-boundary value problems for second-order parabolic equations (35K20) 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) Semilinear parabolic equations (35K58)

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Cites Work

• Unnamed Item
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• Space-time finite element methods for parabolic problems
• Boundary integral operators for the heat equation
• Least-squares finite element methods
• Space-time \(hp\)-approximation of parabolic equations
• \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates
• Theory and practice of finite elements.
• Coercive space-time finite element methods for initial boundary value problems
• An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems
• A short note on plain convergence of adaptive least-squares finite element methods
• Space-time isogeometric analysis of parabolic evolution problems
• Convergence of natural adaptive least squares finite element methods
• Convergence and Optimality of Adaptive Least Squares Finite Element Methods
• Space-time adaptive wavelet methods for parabolic evolution problems
• A convergence proof for adaptive finite elements without lower bound
• Space-Time Adaptive Wavelet Methods for Optimal Control Problems Constrained by Parabolic Evolution Equations
• An adaptive least squares mixed finite element method for the stress-displacement formulation of linear elasticity
• The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Finite Element Methods for Navier-Stokes Equations
• First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
• An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates
• Time-Parallel Iterative Solvers for Parabolic Evolution Equations
• Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems
• Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
• Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
• Dörfler marking with minimal cardinality is a linear complexity problem
• The h‐p version of the finite element method for parabolic equations. II. The h‐p version in time
• Uniform preconditioners for problems of negative order
• Collective marking for adaptive least-squares finite element methods with optimal rates
• New a priori analysis of first‐order system least‐squares finite element methods for parabolic problems
• Fractional Space-Time Variational Formulations of (Navier--) Stokes Equations
• A time dependent Stokes interface problem: well-posedness and space-time finite element discretization
• An improved error bound for reduced basis approximation of linear parabolic problems
• The completion of locally refined simplicial partitions created by bisection
• The Mathematical Theory of Finite Element Methods
• First-order system least squares with inhomogeneous boundary conditions
• Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems