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:
a_{s}(u_{h},v_{h})
:=
å
T Î T
d_{T }(b.Ñu_{h
}+
cu_{h},
b.Ñv_{h})_{T}
and l_{s}(v_{h}):=
å
T Î T
d_{T }(f,
b.Ñv_{h})_{T
},
Here T is a triangle/tetrahedron of the mesh T,
and d_{T} ³
0 is a user-chosen piecewise constant parameter. Often we set d_{T}=k_{d}Ö{S_{T}}
where S_{T} is the area of the triangle T or d_{T}=
k_{d}V_{T
}^{1/3},
where V_{T} is the volume of the tetrahedron T.
Then the equation is
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.