<i>L^∞(L²)</i>and<i>L^∞(L^∞)</i>error estimates for mixed methods for integro-differential equations of parabolic type

Abstract

Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T; L∞(Ω)2), Ω in , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T; L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation of u in L∞ (0,T;L∞(Ω)) and p in L∞(0,T;L∞(Ω)2.