Isogeometric Analysis Approximation of Linear Elliptic Equations with L1 Data

Authors

  • Yibour Corentin Bassonon Université Norbert ZONGO
  • Arouna Ouedraogo Université Norbert Zongo

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i1.4674

Keywords:

Isogeometric analysis, NURBS approximation, L^1 data, renormalized solution

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 W01,q(\Omega),  1 <= q < d/(d-1) . We also prove some error estimates and include numerical tests for data with low smoothness.

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Published

2023-01-29

Issue

Section

Nonlinear Analysis

How to Cite

Isogeometric Analysis Approximation of Linear Elliptic Equations with L1 Data. (2023). European Journal of Pure and Applied Mathematics, 16(1), 404-417. https://doi.org/10.29020/nybg.ejpam.v16i1.4674

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