Stability, analyticity and maximal regularity of semidiscrete isoparametric finite element solutions of parabolic equations in curvilinear polyhedra

In this paper, we investigate the isoparametric finite element semidiscretization for a parabolic problem on a curvilinear polyhedral domain Ω ⊆ R N \Omega \subseteq \mathbb {R}^N with homogeneous Dirichlet boundary condition. The domain Ω \Omega may include nonconvex corners, i.e., with edge openings possibly greater than π \pi . We establish the analyticity and maximal regularity of the discrete semigroup by employing a transformation method to address the domain perturbation effect Ω ≠ Ω h \Omega \neq \Omega _h . As an application of the logarithmically quasi-maximal L ∞ L^\infty -regularity, we derive a quasi-optimal maximum-norm error estimate for the semidiscrete isoparametric finite element methods on curvilinear polyhedral domains with edge openings smaller than π \pi , which includes a term of quasi-optimal order due to domain perturbation.