FEM1D_LAGRANGE
1D Finite Element Code Using Lagrange Basis Polynomials

FEM1D_LAGRANGE is a C++ library which sets up the matrices and vectors associated with the finite element method (FEM) solution of a boundary value problem (BVP) -u''+u=f(x), using Lagrange basis polynomials.

Licensing:

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

Languages:

FEM1D_LAGRANGE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Programs:

FEM1D, a C++ program which applies the finite element method (FEM) to a 1D linear two point boundary value problem (BVP).

LAGRANGE_INTERP_1D, a C++ library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

Source Code:

• fem1d_lagrange.cpp, the source code.
• fem1d_lagrange.hpp, the include file.
• fem1d_lagrange.sh, BASH commands to compile the source code.

Examples and Tests:

• fem1d_lagrange_prb.cpp, a sample calling program.
• fem1d_lagrange_prb.sh, BASH commands to compile and run the sample program.
• fem1d_lagrange_prb_output.txt, the output file.

List of Routines:

• FEM1D_LAGRANGE_STIFFNESS evaluates the Lagrange polynomial stiffness matrix.
• LAGRANGE_DERIVATIVE evaluates the Lagrange basis derivative.
• LAGRANGE_VALUE evaluates the Lagrange basis polynomials.
• LEGENDRE_SET sets abscissas and weights for Gauss-Legendre quadrature.
• R8MAT_FS factors and solves a system with one right hand side.
• R8VEC_LINSPACE creates a vector of linearly spaced values.
• R8VEC_PRINT prints an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.