FEM1D_PMETHOD
P-Method Finite Element Method for 1D problem.

FEM1D_PMETHOD is a C++ program which applies the p-method version of the finite element method to a two point boundary value problem in one spatial dimension.

Licensing:

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

Languages:

FEM1D_PMETHOD 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:

FEM1D, a data directory which contains examples of 1D FEM files, three text files that describe a 1D finite element model;

FEM1D, a C++ program which applies the finite element method to a linear two point boundary value problem in a 1D region.

FEM1D_ADAPTIVE, a C++ program which applies the finite element method to a linear two point boundary value problem in a 1D region, using adaptive refinement to improve the solution.

FEM1D_BVP_LINEAR, a C++ program which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.

FEM1D_HEAT_STEADY, a C++ program which uses the finite element method to solve the steady (time independent) heat equation in 1D.

FEM1D_NONLINEAR, a C++ program which applies the finite element method to a nonlinear two point boundary value problem in a 1D region.

FEM1D_PACK, a C++ library which contains utilities for 1D finite element calculations.

FEM1D_PROJECT, a C++ program which projects data into a finite element space, including the least squares approximation of data, or the projection of a finite element solution from one mesh to another.

FEM1D_SAMPLE, a C++ program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.

Reference:

1. Hans Rudolf Schwarz,
   Finite Element Methods,
   Academic Press, 1988,
   ISBN: 0126330107,
   LC: TA347.F5.S3313.
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,
   LC: TA640.2.Z54

Source Code:

• fem1d_pmethod.cpp, the source code.
• fem1d_pmethod.sh, commands to compile the source code.

Examples and Tests:

• fem1d_pmethod_output.txt, the printed output from a run of the program.

List of Routines:

• MAIN is the main program for FEM1D_PMETHOD.
• ALPBET calculates the coefficients in the recurrence relationship.
• EXACT compares the computed and exact solutions.
• FF evaluates the right hand side function F(X) at any point X.
• ORTHO tests the basis functions for orthogonality.
• OUT prints out the computed solution.
• PHI evaluates the I-th basis function at the point X.
• PP returns the value of the coefficient function P(X).
• QUAD returns the abscissas and weights for gaussian quadrature on [-1,1].
• QQ returns the value of the coefficient function Q(X).
• SOL solves a linear system for the finite element coefficients.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UEX returns the value of the exact solution at a point X.

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