Field-consistency: Toward a science of constrained multi-strain-field finite element formulations

The finite element method has progressed rapidly from simple engineering principles through rigorous mathematical formalizations to become a body of engineering knowledge incorporating well defined13; conceptual schemes and operational procedures. However, it still lacks the self-criticality needed for a falsifiable scientific basis. In this paper, we describe an additional conceptual scheme called field-consistency, and demonstrate new methodology and terminology that helps to clear up an area of the finite element method that had13; remained difficult to understand for some time, and which enhances the predictive capabilities of error analysis of the method. This paper is also in a limited sense, an essay on how the processes of the method of Science are seen to work in this area of engineering know-how