diff --git a/doc/texinfo/gmsh.texi b/doc/texinfo/gmsh.texi index c2917192ad4d3c50e6520225f254add789ccb8fd..fd2ac661c36bd602f1b2ab0906461f54c3140beb 100644 --- a/doc/texinfo/gmsh.texi +++ b/doc/texinfo/gmsh.texi @@ -3133,6 +3133,42 @@ with the edges). @item 19 13-node second order pyramid (5 nodes associated with the vertices and 8 with the edges). +@item 20 +9-node third order incomplete triangle (3 nodes associated with the vertices, 6 +with the edges) +@item 21 +10-node third order triangle (3 nodes associated with the vertices, 6 +with the edges, 1 with the face) +@item 22 +12-node fourth order incomplete triangle (3 nodes associated with the vertices, 9 +with the edges) +@item 23 +15-node fourth order triangle (3 nodes associated with the vertices, 9 +with the edges, 3 with the face) +@item 24 +15-node fifth order incomplete triangle (3 nodes associated with the vertices, 12 +with the edges) +@item 25 +21-node fifth order complete triangle (3 nodes associated with the vertices, 12 +with the edges, 6 with the face) +@item 26 +4-node third order edge (2 nodes associated with the vertices, 2 +internal to the edge) +@item 27 +5-node fourth order edge (2 nodes associated with the vertices, 3 +internal to the edge) +@item 28 +6-node fifth order edge (2 nodes associated with the vertices, 4 +internal to the edge) +@item 29 +20-node third order tetrahedron (4 nodes associated with the vertices, +12 with the edges, 4 with the faces) +@item 30 +35-node fourth order tetrahedron (4 nodes associated with the vertices, +18 with the edges, 12 with the faces, 1 in the volume) +@item 31 +56-node fifth order tetrahedron (4 nodes associated with the vertices, +24 with the edges, 24 with the faces, 4 in the volume) @end table See below for the ordering of the nodes. @@ -3342,27 +3378,27 @@ are defined as follows. @smallexample @group -Line: Line3: +Line: Line3: Line4: -0----------1 --> u 0-----2----1 +0----------1 --> u 0-----2----1 0----2----3----1 @end group @end smallexample @smallexample @group -Triangle: Triangle6: - -v -^ -| -2 2 -|`\ |`\ -| `\ | `\ -| `\ 5 `4 -| `\ | `\ -| `\ | `\ -0----------1 --> u 0-----3----1 +Triangle: Triangle6: Triangle9/10: Triangle12/15: + +v +^ 2 +| | \ +2 2 2 9 8 +|`\ |`\ | \ | \ +| `\ | `\ 7 6 10 (14) 7 +| `\ 5 `4 | \ | \ +| `\ | `\ 8 (9) 5 11 (12) (13) 6 +| `\ | `\ | \ | \ +0----------1 --> u 0-----3----1 0---3---4---1 0---3---4---5---1 @end group @end smallexample @@ -3393,8 +3429,8 @@ Tetrahedron: Tetrahedron10: . ,/ / - 2 2 - ,/|`\ ,/|`\ + 2 2 + ,/|`\ ,/|`\ ,/ | `\ ,/ | `\ ,/ '. `\ ,6 '. `5 ,/ | `\ ,/ 8 `\ @@ -3479,6 +3515,18 @@ Pyramid: Pyramid13: Pyramid14: @end group @end smallexample +The nodes of a curved element are numbered in the following order: +@itemize -- +@item the element principal vertices; +@item the internal nodes for each edge; +@item the internal nodes for each face; +@item the volume internal nodes. +@end itemize + +The numbering for face and volume internal nodes is recursive, ie. the +numbering follows that of the nodes of an embedded face / volume. The +higher order nodes are assumed to be equispaced on the element. + @c ------------------------------------------------------------------------- @c Legacy formats @c -------------------------------------------------------------------------