A novel bubble function scheme for the finite element solution of engineering flow problems
YazdaniAlireza
2018
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.]