On a compact mixed-order finite element for solving the three-dimensional incompressible Navier–Stokes equations

✍ Scribed by Morten M. T. Wang; Tony W. H. Sheu

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 134 KB
• Volume: 25
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19970915)25:5<513::aid-fld573>3.0.co;2-i

✦ Synopsis

Our work is an extension of the previously proposed multivariant element. We assign this re®ned element as a compact mixed-order element in the sense that use of this element offers a much smaller bandwidth. The analysis is implemented on quadratic hexahedral elements with a view to analysing a three-dimensional incompressible viscous ¯ow problem using a method formulated within the mixed ®nite element context. The idea of constructing such a stable element is to bring the marker-and-cell (MAC) grid lay-out to the ®nite element context. This multivariant element can thus be classi®ed as a discontinuous pressure element. We have several reasons for advocating the proposed multivariant element. The primary advantage gained is its ability to reduce the bandwidth of the matrix equation, as compared with its univariant counterparts, so that it can be effectively stored in a compressed row storage (CRS) format. The resulting matrix equation can be solved ef®ciently by a multifrontal solver owing to its reduced bandwidth. The coding is, however, complicated by the appearance of restricted degrees of freedom at mid-face nodes. Through analytic study this compact multivariant element has a marked advantage over the multivariant element of Gupta et al. in that both bandwidth and computation time have been drastically reduced.