### A P-VERSION TWO LEVEL SPLINE METHOD FORSEMI-LINEAR ELLIPTIC EQUATIONS

Xinping Shao, Danfu Han, Xianliang Hu

1. Deptartment of Mathematics, Zhejiang University, Hangzhou 310027, China
• Received:2011-07-11 Revised:2012-03-16 Online:2012-09-15 Published:2012-09-24
• Supported by:

We are grateful to the anonymous referees for their comments and suggestions, which help a lot in improving the quality of this paper. This work is supported by National Natural Science Foundation of China(No.11071216 and No.11101361).

Xinping Shao, Danfu Han, Xianliang Hu. A P-VERSION TWO LEVEL SPLINE METHOD FORSEMI-LINEAR ELLIPTIC EQUATIONS[J]. Journal of Computational Mathematics, 2012, 30(5): 544-554.

A novel two level spline method is proposed for semi-linear elliptic equations, wherethe two level iteration is implemented between a pair of hierarchical spline spaces withdifferent orders. The new two level method is implementation in a manner of p-adaptivity.A coarse solution is obtained from solving the model problem in the low order spline space,and the solution with higher accuracy are generated subsequently, via one step Newtonor monidifed Newton iteration in the high order spline space. We also derive the optimalerror estimations for the proposed two level schemes. At last, the illustrated numericalresults confirm our error estimations and further research topics are commented.

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