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Discrete maximal parabolic regularity for Galerkin finite element methods

2016; Springer Science+Business Media; Volume: 135; Issue: 3 Linguagem: Inglês

10.1007/s00211-016-0821-2

0945-3245

Dmitriy Leykekhman, Boris Vexler,

Numerical methods in engineering

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, in establishing optimal a priori error estimates in non-Hilbertian norms without unnatural coupling of spatial mesh sizes with time steps.