Superconvergence of the function value for pentahedral finite elements for an elliptic equation with varying coefficients
Abstract In this article, for an elliptic equation with varying coefficients, we first derive an interpolation fundamental estimate for the P 2 ( x , y ) ⊗ P 2 ( z ) $\mathcal{P}_{2}(x,y)\otimes \mathcal{P}_{2}(z)$ pentahedral finite element over uniform partitions of the domain. Then combined with...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-019-01318-y |
| Summary: | Abstract In this article, for an elliptic equation with varying coefficients, we first derive an interpolation fundamental estimate for the P 2 ( x , y ) ⊗ P 2 ( z ) $\mathcal{P}_{2}(x,y)\otimes \mathcal{P}_{2}(z)$ pentahedral finite element over uniform partitions of the domain. Then combined with the estimate for the W 2 , 1 $W^{2,1}$ -seminorm of the discrete Green function, superconvergence of the function value between the finite element approximation and the corresponding interpolant to the true solution is given. |
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| ISSN: | 1687-2770 |