Isogeometric Analysis approximation of linear elliptic equations with L1 data

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Résumé

Isogeometric Analysis (IgA) is a recent technique for the discretization of Partial Dif-
ferential Equations (PDEs). The main feature of the method is the ability to maintain the same
exact description of the computational geometry domain throughout the analysis process, includ-
ing 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(Ω), we prove that the unique solution of the discrete problem converges to
the unique renormalized solution in W^1,q0 (Ω), 1 ≤q<d−1 . We also prove some error estimates
and include numerical tests for data with low smoothness.

Mots-clés

Isogeometric analysis, NURBS approximation, L1 data, renormalized solution