Discrete maximal parabolic regularity for Galerkin finite element methods

Abstract

The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the time discontinuous Galerkin solution of linear parabolic equations. Such estimates have many applications. They are essential, for example, for establishing optimal a priori error estimates in non- Hilbertian norms without unnatural coupling of spatial mesh sizes with time steps.

References in corpus (2)

• Pointwise best approximation results for Galerkin finite element solutions of parabolic problems
• Maximal ${\mathbf{L}}^{\mathbf{p}}$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra

Cited by in corpus (10)

• Pointwise best approximation results for Galerkin finite element solutions of parabolic problems
• Optimal Error Estimates for Fully Discrete Galerkin Approximations of Semilinear Parabolic Equations
• Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem s
• Global and interior pointwise best approximation results for the gradient of Galerkin solutions for parabolic problems
• Discrete maximal regularity of time-stepping schemes for fractional evolution equations
• Error estimates for finite element discretizations of the instationary Navier-Stokes equations
• Discrete maximal regularity and the finite element method for parabolic equations
• Maximal regularity of multistep fully discrete finite element methods for parabolic equations
• Fully Discrete Pointwise Smoothing Error Estimates for Measure Valued Initial Data
• Fully discrete best approximation type estimates in $L^{\infty }(I;L^2(\Omega {)}^d)$ for finite element discretizations of the transient Stokes equations