A novel bubble function scheme for the finite element solution of engineering flow problems

This thesis is devoted to the study of some difficulties of practical implementation of finite element solution of differential equations within the context of multi-scale engineering flow problems. In particular, stabilized finite elements and issues associated with computer implementation of these schemes are discussed and a novel technique towards practical implementation of such schemes is presented. The idea behind this novel technique is to introduce elemental shape functions of the polynomial forms that acquire higher degrees and are optimized at the element level, using the least squares minimization of the residual. This technique provides a practical scheme that improves the accuracy of the finite element solution while using crude discretization. The method of residual free bubble functions is the point of our departure. [Continues.]