摘要
在Poisson方程的求解域Ω存在一致的三角剖分,并且相邻两初始单元构成平行四边形的假设下,证明了若Poisson方程的解u属于H^6(Ω),那么二次有限元的误差有h^4的渐近展开.基于误差的渐近展开,可以利用h^4-Richardson外推进一步提高数值解的精度阶,并且能够得到一个后验误差估计.最后,一个数值算例验证了理论分析.
Suppose that there exists a uniform triangular partition on the domain Ω, and two adjacent elements form a parallelogram, then it is Proven that approximation error of quadratic finite element has asymptotic expansion with power h^4, if solution u of Poisson equation belongs to H^6（Ω）. By virtue of ha-Richardson extrapolation based on the asymptotic expansion, the authors not only the accuracy order of the approximation is improved, but also a posteriori error estimation is given. A numerical example demonstrates these theoretical results.
出处
《系统科学与数学》
CSCD
北大核心
2008年第3期340-349,共10页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(10671136)
教育部博士点基金资助课题.
关键词
二次有限元
渐近展开
外推
后验估计
Quadratic finite element, asymptotic expansion, extrapolation, posteriori error.
