Superconvergence of a finite element approximation to the solution of a sobolev equation in a single space variable

Douglas N. Arnold; Jim Douglas; Vidar Thome

doi:10.1090/S0025-5718-1981-0595041-4

Superconvergence of a finite element approximation to the solution of a sobolev equation in a single space variable

Douglas N. Arnold, Jim Douglas, Vidar Thome

Mathematics

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73 Scopus citations

Abstract

A standard Galerkin method for a quasilinear equation of Sobolev type using continuous, piecewise-polynomial spaces is presented and analyzed. Optimal order error estimates are established in various norms, and nodal superconvergence is demonstrated. Discretization in time by explicit single-step methods is discussed.

Original language	English (US)
Pages (from-to)	53-63
Number of pages	11
Journal	Mathematics of Computation
Volume	36
Issue number	153
DOIs	https://doi.org/10.1090/S0025-5718-1981-0595041-4
State	Published - Jan 1981

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title = "Superconvergence of a finite element approximation to the solution of a sobolev equation in a single space variable",

abstract = "A standard Galerkin method for a quasilinear equation of Sobolev type using continuous, piecewise-polynomial spaces is presented and analyzed. Optimal order error estimates are established in various norms, and nodal superconvergence is demonstrated. Discretization in time by explicit single-step methods is discussed.",

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AB - A standard Galerkin method for a quasilinear equation of Sobolev type using continuous, piecewise-polynomial spaces is presented and analyzed. Optimal order error estimates are established in various norms, and nodal superconvergence is demonstrated. Discretization in time by explicit single-step methods is discussed.

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Superconvergence of a finite element approximation to the solution of a sobolev equation in a single space variable

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