ANALYTICITY, MAXIMAL REGULARITY AND MAXIMUM-NORM STABILITY OF SEMI-DISCRETE FINITE ELEMENT SOLUTIONS OF PARABOLIC EQUATIONS IN NONCONVEX POLYHEDRA

摘要

In general polygons and polyhedra, possibly nonconvex, the analyticity of the finite element heat semigroup in the L-q-norm, 1 <= q <= infinity, and the maximal L-p-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 maximum-norm stability of the Ritz projection, which currently is known to hold for general polygonal domains and convex polyhedral domains.