FROM THE INDIVIDUAL ELEMENT TEST TO FINITE-ELEMENT TEMPLATES - EVOLUTION OF THE PATCH TEST

This paper starts a sequence of three articles that follow an unconven tional approach in finite element research. The ultimate objective is to construct :high-performance elements and element-level error estima tors for those elements. The approach takes off From our previous work in high-performance elements and culminates with the development of f inite element templates. The present paper concentrates on the patch t est and evolved versions of the test that have played a key role in th is research. Following a brief review of the historical roots, we pres ent the Individual Element Test (IET) of Bergan and Hanssen in an expa nded context that encompasses several important classes of new element s. The relationship of the IET to the multielement forms A, B and C of the patch test and to the single-element test are investigated. An im portant consequence of the IET application is that the element stiffne ss equations decompose naturally into basic and higher-order parts. Th e application of this decomposition to the ''sanitization' of the non- convergent BCIZ element is described and verified with numerical exper iments. Two sequel papers in preparation are subtitled 'the algebraic approach' and 'element-level error estimation'. These apply the fundam ental decomposition to the derivation of templates for specific mechan ical elements and to the construction of element-level error estimator s, respectively.