Error analysis of a coupled finite--infinite element method for an exterior Poisson problem

Authors:
Chunxiong Zheng
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China and Institut für Numerische Mathematik, Universität Münster, Germany
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

An error estimate is presented for the numerical approximation to an exterior problem of the Poisson equation when a coupled finite-infinite element method is employed in the computation. This estimate involves not only the size h and the order p of the quasiuniform finite element approximation, but also the radius R of the computational domain covered with finite elements and the number N of the radial terms of infinite elements. Numerical tests are performed, and the results partly validate the theoretical analysis.