A two-grid algorithm based on expanded mixed element discretizations for strongly nonlinear elliptic equations
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.
KeywordsTwo-grid method Nonlinear elliptic equations Expanded mixed finite element Error estimates
Mathematics Subject Classifications (2010)65N12 65N15 65N30
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