【作者】 安静；

【导师】 杨一都； 庞之垣；

【作者基本信息】 贵州师范大学 ， 计算数学， 2005， 硕士

【摘要】 关于有限元问题的迭代校正解收敛性海内外有多项成果,参见([1],[2],[3],[4])。其中[3],[4]中分别利用三角形元上插值算子的压缩性质和矩形元上插值算子的压缩性质证明了标准的椭圆方程线性有限元迭代校正解收敛于 petrov-Galerkin 近似解。然而,我们是否能对较一般的微分方程讨论其插值算子的压缩性呢?本论文在一维情形下研究了常系数和变系数两点边值问题,尤其是对奇异两点边值问题插值算子的压缩性质进行了讨论,证明了其插值算子的压缩性及其有限元迭代校正解收敛,并分别给出了数值例子,除此之外,还对一次与三次和二次与四次插值算子之间的压缩性作了讨论。更多还原

【Abstract】 There have been many results about the convergence of iterateddefect correction solutions for finite elements problems ( [1], [2], [3], [4]).In [3-4], the authors have proved that the iterated defect correction oflinear finite element solution for standard elliptic problems converges tothe petrov-Galerkin approximation solution by using the so-calledcontractivity of the interpolation operator for triangular and rectangularelements.Howerer, can we discuss the so-called contractivity of theinterpolation operator for general differential equations? The paperstudied two-point boundary value problems of constant and variablecoefficient in one dimension, especially the singular two-point boundaryvalue problems, and proved the so-called contractivity of linear finiteelement iterated defect correction solutions, and present some numericalexamples. In addition, We also discuss the so-called contractivity betweenlinear and cubic interpolation operator, quadratic and quartic interpolationoperator.更多还原