Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions

Authors:
R. A. Nicolaides and D.-Q. Wang

Journal:
Math. Comp. **67** (1998), 947-963

MSC (1991):
Primary 65N30, 65N15, 35L50

DOI:
https://doi.org/10.1090/S0025-5718-98-00971-5

MathSciNet review:
1474654

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Abstract: This paper contains error estimates for covolume discretizations of Maxwell's equations in three space dimensions. Several estimates are proved. First, an estimate for a semi-discrete scheme is given. Second, the estimate is extended to cover the classical interlaced time marching technique. Third, some of our unstructured mesh results are specialized to rectangular meshes, both uniform and nonuniform. By means of some additional analysis it is shown that the spatial convergence rate is one order higher than for the unstructured case.

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Additional Information

**R. A. Nicolaides**

Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213

Address at time of publication:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213

Email:
rn0m@andrew.cmu.edu

**D.-Q. Wang**

Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213

Address at time of publication:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716

Email:
dqwang@math.udel.edu

DOI:
https://doi.org/10.1090/S0025-5718-98-00971-5

Keywords:
Maxwell's equations,
covolume schemes,
unstructured meshes,
convergence

Received by editor(s):
September 15, 1995

Received by editor(s) in revised form:
March 25, 1996

Article copyright:
© Copyright 1998
American Mathematical Society