Stability and analyticity in maximum-norm for simplical Lagrange finite element semidiscretizations of parabolic equations with Dirichlet boundary conditions (Q1592353)

By the authors' abstract: Stability and analyticity estimates in maximum-norm are shown for spatially discrete finite element approximations based on simplicial Lagrange elements for the model heat equation with homogeneous Dirichlet boundary conditions. By assumption, the family of partitions is quasiuniform. The bounds are logarithm free and valid in arbitrary dimension and for arbitrary polynomial degree. The work continues an earlier study by \textit{A. H. Schatz}, \textit{V. Thomée}, and \textit{L. B. Wahlbin} [Commun. Pure Appl. Math. 51, No. 11-12, 1349-1385 (1998; Zbl 0932.65103)] in which Neumann boundary conditions were considered.