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

FEM2D_BVP_SERENE is a C++ 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM2D_BVP_LINEAR, a C++ 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 C++ 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 C++ 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.cpp, the source code.
• fem2d_bvp_serene.hpp, the include file.
• fem2d_bvp_serene.sh, BASH commands to compile the source code.

Examples and Tests:

• fem2d_bvp_serene_prb.cpp, a sample calling program.
• fem2d_bvp_serene_prb.sh, BASH commands to compile and run the sample program.
• fem2d_bvp_serene_prb_output.txt, the output file.

List of Routines:

• BASIS_SERENE evaluates the serendipity basis functions.
• BASIS_DX_SERENE differentiates the serendipity basis functions.
• BASIS_DY_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 C++ source codes.