A P-Version Two Level Spline Method for Semi-Linear Elliptic Equations

Abstract

A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implemented 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 is generated subsequently, via one step Newton or modified Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.