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Pointwise superconvergence of the gradient for the linear tetrahedral element. (English) Zbl 0807.65112

The author extends the results of his thesis [Gradient superconvergence in the finite element method with applications to planar linear elasticity, Ph.D. Thesis, Brunel University (1988)] on gradient superconvergence over linear triangular finite elements in two dimensions to linear tetrahedral elements in three dimensions, for approximations to the solutions of selfadjoint second-order elliptic boundary value problems with variable coefficients. He also extends the work of V. Kantchev and R. D. Lazarov [Optimal algorithms, Proc. Int. Symp., Blagoevgrad/Bulg. 1986, 172-182 (1986; Zbl 0672.65088)] on linear tetrahedral elements from the average sense of the \(L_ 2\) norm to the pointwise sense of the \(L_ \infty\) norm, to include also the case of problems with variable coefficients.
The author restricts the discussion to problems posed in a rectangular block domain, partitioned by a fully uniform tetrahedral finite element mesh.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Citations:

Zbl 0672.65088
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References:

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