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DOI: 10.23952/cot.2023.36
Received June 28, 2022; Accepted April 26, 2023; Published July 24, 2023
Abstract. We discuss in this article a method for the numerical solution of a linear bi-harmonic problem arising from inverse source problems, like those in electroencephalography. In order to solve this bi-harmonic problem using low order Lagrange finite element approximations, we reformulate it as a functional equation associated with a linear boundary operator of the Steklov-Poincaré type. This boundary equation is well-suited to solution by a conjugate gradient algorithm, requiring the solution of two second order linear elliptic problems per iteration. The performance of our methodology is validated via the solution of test problems for simple and complex 2D geometries, disk-shaped domains in particular.
How to Cite this Article:
R. Glowinski, D.A. León-Velasco, L.H. Juérez-Valencia, J.J. Conde-Mones, J.J. Oliveros-Oliveros, A boundary operator approach for the solution of a biharmonic problem from inverse source problems, Commun. Optim. Theory 2023 (2023) 36.