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

Authors:
Douglas N. Arnold, Jim Douglas and Vidar Thomée

Journal:
Math. Comp. **36** (1981), 53-63

MSC:
Primary 65N30; Secondary 35K70

DOI:
https://doi.org/10.1090/S0025-5718-1981-0595041-4

MathSciNet review:
595041

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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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DOI:
https://doi.org/10.1090/S0025-5718-1981-0595041-4

Article copyright:
© Copyright 1981
American Mathematical Society