REMARKS ON THE PRESSURE ERROR-ESTIMATES FOR THE PROJECTION METHODS

被引:52
作者
SHEN, J
机构
[1] Department of Mathematics, Penn State University, University Park, Pennsylvania
关键词
Mathematics Subject Classification (1991): 35A40; 65J15;
D O I
10.1007/s002110050042
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The purpose of this note is to correct some errors in the proofs of pressure error estimates in [1] and [2]. The origin of the errors is the following incorrect inequality (1) c2\\u\\-1(2) less-than-or-equal-to (A-1u,u), (see (2.1) in [11 and (2.7) in [2]), which the author incorrectly derived by identifying \\u\\V' with \\u\\-1 for u is-an-element-of H.2 The correct inequality is: (2) c2\\u\\V'2 less-than-or-equal-to (A-1 u,u). However, the incorrect proofs induced by the error (1) can all be fixed as indicated below. More precisely, the proofs for the velocity error estimates in [ 1, 2] are all valid provided some minor changes of notations; the pressure error estimates still hold, but their proofs necessitate some additional estimates. In summary, all the results presented in [1, 2] remain valid provided some additional regularity.assumptions on the exact solution are made. In the following we provide the details for the aforementioned modifications and corrections.
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页码:513 / 520
页数:8
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