MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a
FORTRAN program for the solution of second order linear elliptic
partial differential equations of the form
d du d du
- -- (p --) - -- (q --) + ru = f in D
dx dx dy dy
with boundary conditions of the form
u = g on d1
du dy du dx
p -- -- - q -- -- + cu = g on d2
dx ds dy ds
where p>0, q>0, r, f, c and g are functions of x and y, D
is a polygonal domain in R^2 (possibly with holes), d1 U d2 is
the boundary of D, and d/ds is differentiation with respect to a
counterclockwise parameterization of the boundary (x(s),y(s)).
The second form of the boundary condition, called the natural
boundary condition, reduces to the Neuman boundary condition
when p=q=1.
MGGHAT uses a finite element method with linear, quadratic or
cubic elements (user selectable) over triangles. The adaptive
refinement via newest vertex bisection and the multigrid iteration
are both based on a hierarchical basis formulation. Run time and
a posteriori graphical displays are made with gnuplot.