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An explicit analysis of Stummel's patch test examples
Author(s) -
Shi ZhongCi
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200705
Subject(s) - constructive , convergence (economics) , mathematics , norm (philosophy) , calculus (dental) , mathematical analysis , mathematical optimization , computer science , medicine , dentistry , process (computing) , political science , law , economics , economic growth , operating system
A constructive approach for the treatment of Stummel's examples to the patch test is presented, together with generalizations of these examples. The strange convergence phenomenon of nonconforming approximations is discussed in detail, and a kind of modified variational equation for remedying these defects is introduced. Our variational equation uses a combination of hybrid and penalty methods that define a convergent procedure with optimal order of convergence to the exact solution with respect to a mesh‐dependent norm.