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

Author:

Arnold Douglas N.,Douglas Jim,Thomée Vidar

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference20 articles.

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2. J. L. Bona, W. G. Pritchard & L. R. Scott, "A comparison of laboratory experiments with a model equation for water waves." (To appear.)

3. The initial-value problem for the Korteweg-de Vries equation;Bona, J. L.;Philos. Trans. Roy. Soc. London Ser. A,1975

4. Numerical study of the regularized long-wave equation. I. Numerical methods;Eilbeck, J. C.;J. Comput. Phys.,1975

5. Numerical solution of Sobolev partial differential equations;Ewing, Richard E.;SIAM J. Numer. Anal.,1975

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