FEM2D_BVP_SERENE
Finite Element Method, 2D, Boundary Value Problem, Serendipity Elements

FEM2D_BVP_SERENE is a FORTRAN90 program which applies the finite element method, with serendipity elements, to a 2D boundary value problem over a rectangle.

The boundary value problem (BVP) that is to be solved has the form:

        - d/dx ( a(x,y) * du/dx ) - d/dy ( a(x,y) * du/dy ) + c(x,y) * u(x,y) = f(x,y)
      

Zero boundary conditions are imposed on the boundary of R.

The MATLAB "gallery()" command can produce a copy of the Wathen matrix, which arises as a weighted sum of elementary mass matrices associated with a grid of serendipity elements.

Licensing:

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

Languages:

FEM2D_BVP_SERENE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM2D_BVP_LINEAR, a FORTRAN90 program which applies the finite element method (FEM), with piecewise linear elements, to a 2D boundary value problem (BVP) over a rectangle, and compares the computed and exact solutions with the L2 and seminorm errors.

FEM2D_BVP_QUADRATIC, a FORTRAN90 program which applies the finite element method (FEM), with piecewise quadratic elements, to a 2D boundary value problem (BVP) over a rectangle, and compares the computed and exact solutions with the L2 and seminorm errors.

WATHEN, a FORTRAN90 library which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, Linpack, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

Source Code:

• fem2d_bvp_serene.f90, the source code.

Examples and Tests:

• fem2d_bvp_serene_test.f90, a sample calling program.
• fem2d_bvp_serene_test.txt, the output file.

List of Routines:

• BASIS_SERENE evaluates the serendipity basis functions.
• BASISD_SERENE differentiates the serendipity basis functions.
• FEM2D_BVP_SERENE solves boundary value problem on a rectangle.
• FEM2D_BVP_SERENE_NODE_NUM counts the number of nodes.
• FEM2D_H1S_ERROR_SERENE: seminorm error of a finite element solution.
• FEM2D_L1_ERROR_SERENE: l1 error norm of a finite element solution.
• FEM2D_L2_ERROR_SERENE: L2 error norm of a finite element solution.
• NOT1 evaluates a factor for serendipity basis functions.
• NOT1D differentiates a factor for serendipity basis functions.
• NOT2 evaluates a factor for serendipity basis functions.
• NOT2DX evaluates a factor for serendipity basis functions.
• NOT2DY evaluates a factor for serendipity basis functions.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8MAT_SOLVE2 computes the solution of an N by N linear system.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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