Numerical solution of a one-dimensional inverse problem by the discontinuous Galerkin method

Y. Epshteyn, Tehmina Khan () and B. Rivière

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 7, 1989-2000

Abstract: In this paper, we combine a Tikhonov regularization with a discontinuous Galerkin method to solve an inverse problem in one-dimension. We show that the regularization is simpler than in the case of the inversion using continuous finite elements. We numerically demonstrate that there exist optimal step sizes and polynomial degrees for inversion using the DG method. Numerical results are compared with those obtained by applying the standard finite element method with B-splines as a basis.

Keywords: Inverse problems; Primal discontinuous Galerkin method; Tikhonov regularization (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:7:p:1989-2000

DOI: 10.1016/j.matcom.2008.08.002

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