The gradient superconvergence of the finite volume method for a nonlinear elliptic problem of nonmonotone type
| Autor: | Tie Zhu Zhang, Shuhua Zhang |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Applications of Mathematics. 60:573-596 |
| ISSN: | 1572-9109 0862-7940 |
| DOI: | 10.1007/s10492-015-0112-8 |
| Popis: | We study the superconvergence of the finite volume method for a nonlinear elliptic problem using linear trial functions. Under the condition of C-uniform meshes, we first establish a superclose weak estimate for the bilinear form of the finite volume method. Then, we prove that on the mesh point set S, the gradient approximation possesses the superconvergence: $${\max _{P \in S}}|(\nabla u - \overline \nabla {u_h})(P)| = O({h^2})|\ln h{|^{3/2}}$$ , where $$\overline \nabla $$ denotes the average gradient on elements containing vertex P. Furthermore, by using the interpolation post-processing technique, we also derive a global superconvergence estimate in the H 1-norm and establish an asymptotically exact a posteriori error estimator for the error ‖u − u h ‖1. |
| Databáze: | OpenAIRE |
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