sci.math.research SUNA29, Linearized Quadrilaterals ================================= Two element types were developed as a Unified Numerical Approximation for Ideal Flow: "Staggered Quadrilaterals" and "Patched Quadrilaterals". The former type gives rise to the following set of equations for the quadrilateral as a whole: 3 (y2 - y1).u1 - (x2 - x1).v1 + 4 o ---*--- o 3 (y3 - y2).u2 - (x3 - x2).v2 + | | (y4 - y3).u3 - (x4 - x3).v3 + 4 * * 2 (y1 - y4).u4 - (x1 - x4).v4 = 0 (1) | | (x2 - x1).u1 + (y2 - y1).v1 + 1 o ---*--- o 2 (x3 - x2).u2 + (y3 - y2).v2 + 1 (x4 - x3).u3 + (y4 - y3).v3 + (x1 - x4).u4 + (y1 - y4).v4 = 0 (2) The latter type of ("patched") element resulted in linear relationships between function values: u1 - u2 + u3 - u4 = 0 (3) v1 - v2 + v3 - v4 = 0 (4) Isn't it possible to combine these four equations into the formulation of a new Finite Element for Ideal Flow? That would be simple and straightforward anyway. We tried just that ... And it seems to work! ^^^^^ More later. My vacation is over. Going back to regular activities. Don't worry if you didn't catch up every SUNA article that appeared on the net. I will make this stuff available via kind of Anonymous Ftp or Bulletin Board. Alas, administratium is impeding a quick reaction here. :-) - * Han de Bruijn; Applications&Graphics | "A little bit of Physics * No * TUD Computing Centre; P.O. Box 354 | would be NO idleness in * Oil * 2600 AJ Delft; The Netherlands. | Mathematics" (HdB). * for * E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood