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Asymptotic expansions of finite element solutions to Robin problems in H 3 and their application in extrapolation cascadic multigrid method |
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| Authors: | HongLing Hu ChuanMiao Chen KeJia Pan |
| Affiliation: | 1. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha, 410081, China 2. School of Mathematics and Statistics, Central South University, Changsha, 410075, China 3. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, School of Geosciences and Info-Physics, Central South University, Changsha, 410083, China |
| Abstract: | For the Poisson equation with Robin boundary conditions, by using a few techniques such as orthogonal expansion (M-type), separation of the main part and the finite element projection, we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h 3) for u ∈ H 3. Based on the obtained asymptotic error expansions for linear finite elements, extrapolation cascadic multigrid method (EXCMG) can be used to solve Robin problems effectively. Furthermore, by virtue of Richardson extrapolation, not only the accuracy of the approximation is improved, but also a posteriori error estimation is obtained. Finally, some numerical experiments that confirm the theoretical analysis are presented. |
| Keywords: | finite element Richardson extrapolation Robin problem asymptotic expansion cascadic multigrid method |
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