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1994•Numerical Methods for Partial Differential EquationsRequires access

Superconvergence of finite element approximations to Maxwell's equations

Peter Monk

Open publisher page 51 citations

Abstract

Abstract We study superconvergence of edge finite element approximations to the magnetostatic problem and to the time‐dependent Maxwell system. We show that in special discrete norms there is an increase of one power in the order of convergence of the finite element method compared to error estimates in standard Sobolev norms. Our results are restricted to an orthogonal grid inR3, but the grid may be nonuniform. © 1994 John Wiley & Sons, Inc.

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Abstract We study superconvergence of edge finite element approximations to the magnetostatic problem and to the time‐dependent Maxwell system. We show that in special discrete norms there is an increase of one power in the order of convergence of the finite element method compared to error estimates in standard Sobolev norms. Our results are restricted to an orthogonal grid inR3, but the grid may be nonuniform. © 1994 John Wiley & Sons, Inc.

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Available abstract

Abstract We study superconvergence of edge finite element approximations to the magnetostatic problem and to the time‐dependent Maxwell system. We show that in special discrete norms there is an increase of one power in the order of convergence of the finite element method compared to error estimates in standard Sobolev norms. Our results are restricted to an orthogonal grid inR3, but the grid may be nonuniform. © 1994 John Wiley & Sons, Inc.

Key concepts: Superconvergence, Mathematics, Finite element method, Maxwell's equations, Sobolev space, Mathematical analysis, Convergence (economics), Mixed finite element method

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