TY - JOUR
T1 - A P-Version Two Level Spline Method for Semi-Linear Elliptic Equations
AU - Xinping Shao, Danfu Han & Xianliang Hu
JO - Journal of Computational Mathematics
VL - 5
SP - 544
EP - 554
PY - 2012
DA - 2012/10
SN - 30
DO - http://doi.org/10.4208/jcm.1203-m3813
UR - https://global-sci.org/intro/article_detail/jcm/8449.html
KW - P-version, Two level method, Spline methods, Semi-linear, Error estimation.
AB - <p style="text-align: justify;">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.</p>