Least-square finite element method for electromagnetic fields in 2-D

A least-squares finite element approximation scheme for electromagnetic fields in two-dimensional domains is discussed. Considering the magnetic-field strength \lsH\ls and the vector of the current density \lsJ̃\ls as unknowns, we describe Maxwell's equation as a time-dependent form in three di...

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Bibliographic Details
Published in:Applied mathematics and computation 1993-10, Vol.58 (2), p.143-167
Main Authors: Li, J.S., Yu, Z.Y., Xiang, X.Q., Ni, W.P., Chang, C.L.
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Classical electromagnetism, maxwell equations
Classical field theories
Exact sciences and technology
Physics
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Summary:A least-squares finite element approximation scheme for electromagnetic fields in two-dimensional domains is discussed. Considering the magnetic-field strength \lsH\ls and the vector of the current density \lsJ̃\ls as unknowns, we describe Maxwell's equation as a time-dependent form in three dimensions, then reduce it into two-dimensional steady problems of two categories. Based on the first-order system of partial differential equations, the least-squares method is applied to the finite-element method. The rates of convergence for both \lsH\ls and \lsJ̃\ls achieve optimal order. This method creates an easy way to develop computer software.
ISSN:0096-3003
1873-5649
DOI:10.1016/0096-3003(93)90134-Z