In this paper, a method is described for automatically generating graded un- structured triangular meshes in polygonal domain or tetrahedral meshes in poly- hedral region. For a given set of assigned nodes with the corresponding spacing values, the method will generate a distribution of well-placed nodes on boundary and in the interior of the domain and then give a graded mesh.
The solution of the boundary-vaue problem for non-self-adjoint elliptic equa tions is approximated by Partial Upwind Finite Element method, where all the angles of the triangles a are /2 but the mesh parameter h are arbitrary and which insures the validity of the strongly maximum principle for the discrete prob-lem. The Schwarz alternating method will enable us to break the discrete linear system into several linear subsystems of smaller size and we shall show that the approximate solutions from Schwarz domain decomposition method converge to the exact solution of the linear system geometrically and uniformly.
In this paper a kind of partial upwind finite element method is discussed for two dimensional Burger’s equations. it is shown that the umerical solutions preserve discrete maximum principle. The theoretical analysis of error is also given.
