Discontinuous velocity boundary data for the lid driven cavity flow has long been causing difficulties in both theoretical analysis and numerical simulations. In finite element methods, the variational form for the driven cavity flow is not valid since the velocity is not in H. Hence standard error estimates do not work. By using only W1,r (1 < r < 2) regularity and constructing a continuous ap...

The change in shape of the C. elegans embryo from an ovoid ball of cells into a worm-shaped larva is driven by three events within the cells of the hypodermis (epidermis): (1) intercalation of two rows of dorsal cells, (2) enclosure of the ventral surface by hypodermis, and (3) elongation of the embryo. While the behavior of the hypodermal cells involved in each of these processes differs drama...

Lattice Boltzmann method is relatively new method in the field of computational fluid dynamics. It has been derived from lattice gas automata and is still under development. Basic steps of the LBM (collision, streaming, boundary conditions, macroscopic quantities) will be presented. Comparison with the finite difference method that uses Navier-Stokes equation on a lid driven cavity benchmark te...