Isogeometric Analysis Approximation of Linear Elliptic Equations with L1 Data

Abstract

Isogeometric Analysis (IgA) is a recent technique for the discretization of Partial Differential Equations (PDEs). The main feature of the method is the ability to maintain the same exact description of the computational domain geometry throughout the analysis process, including refinement. In the present paper, we consider, in dimension d >= 2 the Isogeometric Analysis approximation of second order elliptic equations in divergence form with right-hand side in L¹   . We assume that the family of meshes is shape regular and satisfies the discrete maximum principle. When the right-hand side belongs to L¹(\Omega), we prove that the unique solution of the discrete problem converges to the unique renormalized solution in W₀^1,q(\Omega),  1 <= q < d/(d-1) . We also prove some error estimates and include numerical tests for data with low smoothness.