In the framework of a Hilbert triple {V, H, V′} we study the approximation and the regular- ity of parabolic variational inequalities, by a time discretization by means of the backward Euler scheme. Under suitable regularity hypotheses on the data, we prove that the order of convergence in H1(0, T ; H) is 1/2 and the solution belongs to Hs(0, T ; H), ∀ s < 3/2. Moreover, in the case of a symmetric linear operator with L2(0, T ; H) data, we prove the H1/2(0, T ; V )-regularity of the solution with the same error estimate in the “energy norm” of L2(0,T;V)∩L∞(0,T;H).
Approximation and regularity of evolution variational inequalities
SAVARE', GIUSEPPE
1993-01-01
Abstract
In the framework of a Hilbert triple {V, H, V′} we study the approximation and the regular- ity of parabolic variational inequalities, by a time discretization by means of the backward Euler scheme. Under suitable regularity hypotheses on the data, we prove that the order of convergence in H1(0, T ; H) is 1/2 and the solution belongs to Hs(0, T ; H), ∀ s < 3/2. Moreover, in the case of a symmetric linear operator with L2(0, T ; H) data, we prove the H1/2(0, T ; V )-regularity of the solution with the same error estimate in the “energy norm” of L2(0,T;V)∩L∞(0,T;H).File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
