Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem s
Provides a theoretical foundation for error analysis of finite element methods for time-dependent parabolic equations, benefiting numerical analysts working on non-autonomous problems.
The paper establishes discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problems, enabling best approximation results in the L^p(0,T;L^2(Ω)) norm for 1≤p≤∞.
The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent coefficients. Such estimates have many applications. As one of the applications we establish best approximations type results with respect to the $L^p(0,T;L^2(Ω))$ norm for $1\le p\le \infty$.