二阶非线性抛物方程的B样条有限元法

B-Spline Finite Element Method of Second OrderNonlinear Parabolic Equation

首先,用二次B样条有限元法求解Fisher-Kolmogorov(FK)方程,证明半离散格式与全离散格式解的稳定性与收敛性;其次,用Crank-Nicolson方法离散时间变量,得到近似解的收敛阶为O((Δt)^(2)+h^(3));最后,用数值算例验证了理论分析结果及B样条有限元法的有效性.

Firstly,we uesd the quadratic B-spline finite element method to solve the Fisher-Kolmogorov(FK)equation,and proved the stability and convergence of solutions for the semi-discrete scheme and the fully discrete scheme.Secondly,the time variable was discretized by using the Crank-Nicolson method and the convergence order of the approximate solution was O((Δt)^(2)+h^(3)).Finally,the numerical example verified theoretical analysis results and the effectiveness of the B-spline finite element method.