Development of a library of field-consistent finite elements

Although the finite element method has progressed rapidly from simple engineering principles to thorough and rigorous mathematical formalisations, there still exist large areas of uncertainty. We review here, some of the recent progress made in our laboratory to identify and classify a particular problem area in the finite element method, to define its new vocabulary and devise new operational procedures of error analysis based on this conceptual scheme and use this to design and develop and test an entire library of x201C;field-consistentx201D; elements.13