Adaptive Wavelet Finite Element Method for Partial Differential Equation

作者：Tang, Yan; Xiang, Jiawei^*; Xu, Jinyong; Ye, Fangyong; Lan, Yushen

来源：Advanced Science Letters, 2011, 4(8-10): 3151-3154.

DOI：10.1166/asl.2011.1285

• Possion's Equation
• Finite Element Methods
• Adaptivity
• Numerical Simulation

Numerical simulation of two-dimensional Possion's equation based on adaptive wavelet finite element method is proposed. Multi-scale elements based on B-spline wavelet on the interval (BSWI) are constructed to approximate the high gradient right-hand of Possion's problem. The adaptive algorithm is also presented by virtue of traditional adaptive finite element method. Thus finite element solution equation formed by the initial scale can be succeeded in the process of solving finite element equation with the next scale, which is a simple and efficient way. Example of high gradient Possion equation's numerical value with Dirchlet boundary condition further shows that multi-scale BSWI element provides a nested adaptive element with a better approximation capability when solving singularity or high gradient problems.

• 出版日期2011-10
• 单位桂林电子科技大学