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

Arnold, Douglas N.; Douglas, Jim; Thomée, Vidar

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
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by Douglas N. Arnold, Jim Douglas and Vidar Thomée PDF

Math. Comp. 36 (1981), 53-63 Request permission

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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