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Gradient superconvergence post-processing of the tensor-product quadratic pentahedral finite element

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  • In this article, using the well-known Superconvergent Patch Recovery (SPR) method, we present a gradient superconvergence post-processing scheme for the tensor-product quadratic pentahedral finite element approximation to the solution of a general second-order elliptic boundary value problem in three dimensions over fully uniform meshes. The supercloseness property of the gradients between the finite element solution $u_h$ and the tensor-product quadratic interpolation $\Pi u$ is first given. Then we show that the gradient recovered from the finite element solution by using the SPR method is superconvergent to $\nabla u$ at interior vertices.
    Mathematics Subject Classification: Primary: 65N30; Secondary: 65N12.

    Citation:

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