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Superconvergent recovery of the gradient from piecewise linear finite- element approximations. (English) Zbl 0584.65067
The object of this paper is to propose and justify the use of a simple scheme which recovers gradients from the piecewise linear finite element approximation on triangular elements to the solution of a second-order elliptic problem. The recovered gradient is a superconvergent estimate of the true gradient at the midpoints of element edges. A related scheme recovers the gradient at the element centroids.
[Shortened review. The full version is available at request.]
Reviewer: M.Bernadou

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D25 Numerical differentiation
35J25 Boundary value problems for second-order elliptic equations
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