ON A COMPACT MIXED-ORDER FINITE-ELEMENT FOR SOLVING THE 3-DIMENSIONALINCOMPRESSIBLE NAVIER-STOKES EQUATIONS

Our work is an extension of the previously proposed multivariant eleme nt. We assign this refined element as a compact mixed-order element in the sense that use of this element offers a much smaller bandwidth. T he analysis is implemented on quadratic hexahedral elements with a vie w to analysing a three-dimensional incompressible viscous flow problem using a method formulated within the mixed finite element context. Th e idea of constructing such a stable element is to bring the marker-an d-cell (MAC) grid lay-out to the finite element context. This multivar iant element can thus be classified as a discontinuous pressure elemen t. We have several reasons for advocating the proposed multivariant el ement. The primary advantage gained is its ability to reduce the bandw idth of the matrix equation, as compared with its univariant counterpa rts, so that it can be effectively stored in a compressed row storage (CRS) format. The resulting matrix equation can be solved efficiently by a multifrontal solver owing to its reduced bandwidth. The coding is , however, complicated by the appearance of restricted degrees of free dom at mid-face nodes. Through analytic study this compact multivarian t element has a marked advantage over the multivariant element of Gupt a et al. in that both bandwidth and computation time have been drastic ally reduced. (C) 1997 by John Wiley & Sons, Ltd.