Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra

Abstract

In general polygons and polyhedra, possibly nonconvex, the analyticity of the finite element heat semigroup in the Lq-norm, 1 ≤ q ≤ ∞, and the maximal Lp-regularity of semi-discrete finite element solutions of parabolic equations are proved. By using these results, the problem of maximum-norm stability of the finite element parabolic projection is reduced to the maximumnorm stability of the Ritz projection, which currently is known to hold for general polygonal domains and convex polyhedral domains.