On Maximal Regularity Estimates for Discontinuous Galerkin Time-Discrete Methods

DOI10.1137/20m1383781zbMath1529.65051OpenAlexW4206955908MaRDI QIDQ6172652

Charalambos G. Makridakis, Georgios D. Akrivis

Publication date: 20 July 2023

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1383781

zbMATH Keywords

a posteriori error estimatesdiscontinuous Galerkin methodsparabolic equationsmaximal parabolic regularityRadau IIA methodsdiscrete maximal parabolic regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (2)

A posteriori error estimates for Radau IIA methods via maximal parabolic regularity ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022

Cites Work

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• Discrete maximal parabolic regularity for Galerkin finite element methods
• Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
• Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods
• A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces
• Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity
• A posteriori error estimates for Radau IIA methods via maximal parabolic regularity
• A posteriori error analysis for higher order dissipative methods for evolution problems
• Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine
• A-Stable Time Discretizations Preserve Maximal Parabolic Regularity
• A posteriori error estimates for the Crank–Nicolson method for parabolic equations
• Adaptive Finite Element Methods for Parabolic Problems VI: Analytic Semigroups
• A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
• A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations
• Discrete Maximal Parabolic Regularity for Galerkin Finite Element Methods for Nonautonomous Parabolic Problems
• ON WELL-POSEDNESS OF DIFFERENCE SCHEMES FOR ABSTRACT PARABOLIC EQUATIONS INL^P([0,T;E) SPACES]
• Galerkin Finite Element Methods for Parabolic Problems
• A solution to the problem of \(L^p\)-maximal regularity
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity

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