Isogeometric analysis approximation of parabolic problem with right-hand side in L^1

Abstract

In the present paper, we study approximation by a new space-time Iso- geometric Analysis (IgA) method for linear parabolic evolution equation namely ∂u/∂t−div(A∇u)=f in Q=Ω×(0,T). We assume that the physical mesh is quasi-uniform. In addition, the right-hand side f of the problem belongs to L1(Q). We prove that the unique solution of the discrete problem, obtained by the Isogeometric Analysis method, converges in L1(0,T;W1,q(Ω)), for every q with 1 ≤ q < d/d-1, to the unique renormalized solution of the problem.