This scheme is not suitable in the case when a is small compared
with b. Therefore we have to add some stability terms which are
(for piecewise linear trials) as follows:
as(uh,vh)
:=
å
T Î T
dT (b.Ñuh
+
cuh,
b.Ñvh)T
and ls(vh):=
å
T Î T
dT (f,
b.Ñvh)T
,
Here T is a triangle/tetrahedron of the mesh T,
and dT ³
0 is a user-chosen piecewise constant parameter. Often we set dT=kdÖ{ST}
where ST is the area of the triangle T or dT=
kdVT
1/3,
where VT is the volume of the tetrahedron T.
Then the equation is
a(uh,vh)
+ as(uh,vh)
= l(vh)
+ ls(vh).
The finite element solver presents MATLAB procedures for:
· creating geometric models for 2D
and 3D domains;
· mesh generation (with help of Triangle
for 2D and QMG for 3D);
· creating stiffness matrix and solving
the linear system;
· visualization of domains, meshes
and solutions.