sci.math.research

SUNA29, Linearized Quadrilaterals
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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. :-)
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* 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