Nonuniform spatial mesh adaptation using a posteriori error estimates: applications to forward and inverse problems

Abstract In this paper we present an adaptive method for the solution of large scale forward and inverse problems occurring in biomedicine. Specifically, we describe models based on magnetic resonance images of the human thorax that are used to solve electric and potential field imaging problems. We introduce two- and three-dimensional nonuniform spatial mesh adaptation schemes based upon a posteriori error estimates from the finite element approximation, an algorithm that utilizes a minimax theorem based on estimates of the electric and potential fields and a three-dimensional, Delaunay triangulation program. Initial results are presented for two- and three-dimensional models.

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