矩形元上插值算子压缩性质及有限元迭代校正

THE DEFECT ITERATION OF THE FINITE ELEMENT AND THE "CONTRACTIVITY" OF THE INTERPOLATION OPERATOR FOR RECTANGULAR ELEMENTS

本文研究了矩形元上插值算子的性质 ,证明了一维及二维情形下插值算子具有压缩性 ,从而证明了矩形元上有限元迭代校正解收敛 ,并对几种不同类型的 L型区域给出了数值例子 ,最后对三维及三维就以上情形作出了讨论 .

In this paper, we have discussed the approxiamation property of interpolation operator, then we have got and proven its best approxiamations in some general cases. In these cases, we have discussed the property which is so called 'contractivity' of interpolation operator in rectangular elements. At a result ,we have proven that the iterated defect correction is convergent and give some numeric tests as experiments for theory results. We have found a general method to get the best approxiamation property of interpolation operator in Soblev space. For example, we have got ‖I 2u-I 1u‖T≤(17/32)‖I 2u‖ T.As a application, we have got the convergence for defect iteration of the finite elements in rectangular element in two dimensional and three dimensional case.