FEM2D_POISSON_LAKE
A Problem in a Lake-shaped Region for FEM2D_POISSON

FEM2D_POISSON_LAKE is a FORTRAN90 library which defines the geometry of a lake-shaped region, as well as boundary conditions for a given Poisson problem, and is called by FEM2D_POISSON as part of a solution procedure.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

FEM2D_POISSON_LAKE is available in a FORTRAN90 version.

Related Data and Programs:

FEM2D_POISSON, a FORTRAN90 program which solves Poisson's equation on a triangulated region, using the finite element method.

FEM2D_POISSON_ELL, a FORTRAN90 library which defines the geometry of an L-shaped region, as well as boundary conditions for a given Poisson problem, and is called by FEM2D_POISSON as part of a solution procedure.

Reference:

1. Hans Rudolf Schwarz,
   Methode der Finiten Elemente,
   Teubner Studienbuecher, 1980,
   ISBN: 3-519-02349-0.
2. Gilbert Strang, George Fix,
   An Analysis of the Finite Element Method,
   Cambridge, 1973,
   ISBN: 096140888X,
   LC: TA335.S77.
3. Olgierd Zienkiewicz,
   The Finite Element Method,
   Sixth Edition,
   Butterworth-Heinemann, 2005,
   ISBN: 0750663200.

Source Code:

• lake.f90, the user-supplied routines to evaluate the right hand side, linear coefficient, and boundary conditions;
• lake_nodes.txt, a text file containing a list, for each node, of its X and Y coordinates;
• lake_nodes.png, a PNG image of the nodes;
• lake_elements.txt, a text file containing a list, for each element, of the three nodes that compose it;
• lake_elements.png, a PNG image of the element mesh;

Examples and Tests:

• lake.txt, output from a run of the program;
• lake_solution.txt, a text file containing the solution U at each node (X,Y);

List of Routines:

• DIRICHLET_CONDITION sets the value of a Dirichlet boundary condition.
• H_COEF evaluates the coefficient H(X,Y) of DEL U in the Poisson equation.
• K_COEF evaluates the coefficient K(X,Y) of U in the Poisson equation.
• RHS gives the right-hand side of the differential equation.

You can go up one level to the FORTRAN90 source codes.