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Numerical Algorithms

, Volume 70, Issue 1, pp 93–111 | Cite as

A two-grid algorithm based on expanded mixed element discretizations for strongly nonlinear elliptic equations

  • Wei Liu
  • Zhe Yin
  • Jin Li
Original Paper

Abstract

An expanded mixed element method is presented to solve a strongly nonlinear elliptic problem. Existence and uniqueness of approximation solution are analyzed. Error estimates in L q and H s norms are also obtained in this paper. To solve the resulting nonlinear system of equations efficiently, we use a two-grid algorithm to decompose the nonlinear system into a small nonlinear system on a coarse grid with mesh size H and a linear system on a fine grid with mesh size h. It’s shown that the approximation still achieves asymptotically optimal as long as the mesh sizes satisfy H=O(h 1/2). Some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed numerical algorithm.

Keywords

Two-grid method Nonlinear elliptic equations Expanded mixed finite element Error estimates 

Mathematics Subject Classifications (2010)

65N12 65N15 65N30 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematics and Statistics ScienceLudong UniversityYantaiPeople’s Republic of China
  2. 2.School of Mathematical SciencesShandong Normal UniversityJinanPeople’s Republic of China
  3. 3.School of ScienceShandong Jianzhu UniversityJinanPeople’s Republic of China

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