DISCRETE MAXIMAL Lp REGULARITY FOR FINITE ELEMENT OPERATORS.

Let {Ah}h>0 be a family of elliptic finite element operators. Let I = [0, T] and consider the problem u′h(t) - Ahuh(t) = ƒh(t), t ∊ I, uh(0) = 0. In this paper, we show that for 1 < p < ∞ the solution of that problem satisfies the estimate ∥u′h∥Lp(I;Lp(Ω)) + ∥Ahuh∥Lp(I;Lp(Ω)) ≤ C∥ƒh∥Lp(I;Lp(Ω)), where C is independent of the parameter h and ƒh. In this case {Ah}h>0 is said to have discrete maximal Lp regularity. [ABSTRACT FROM AUTHOR]