Finite Element Methods: Session-#44

A subject of great importance in the finite element analysis of a continuum mechanics problem is the selection of particular finite elements and the selection of interpolating function over a typical element. If the Lagrangian (i.e., weighted integral) function appearing under the integral in the element equation contains derivatives up to the (r+1)th order, then to have rigorous assurance of convergence as element sizes decreases and/or the rule of state variable over a typical element becomes more accurate, we must have the following two requirements: 1. Compatibility requirement: At element interfaces, we must have C^r continuity \e 2. Completeness requirement: Within an element, we must have C^(r+1) continuity In this session, how to choose interpolating function over a typical element when the integrand contain derivative of second order is explained in some detail. This situation could come from a second-order ODE when no integration by part is considered. In addition, if the governing equation is of fourth order, then the integration by part will leave the integrand of being second order. \e

• #تحصیلات_و_یادگیری
• #compatibility_require
• #completeness_requiremen
• #convergence_assurance