Discrete maximal L-p regularity for finite element operators

摘要

Let {A(h)}(h > 0) be a family of elliptic finite element operators. Let I = [0, T] and consider the problem u'(h)(t) - A(h)u(h)(t) = f(h)(t), t is an element of I, u(h)(0) = 0. In this paper, we show that for 1 < p < infinity the solution of that problem satisfies the estimate parallel to u'(h)parallel to(Lp(I;Lp(Omega))) + parallel to A(h)u(h)parallel to(Lp(I;Lp(Omega))) <= C parallel to f(h)parallel to(Lp(I;Lp(Omega))), where C is independent of the parameter h and f(h). In this case {A(h)}(h > 0) is said to have discrete maximal Lp regularity.