FEM1D_ODEN
Finite Element Method for 1D Geometry.

FEM1D_ODEN is a FORTRAN77 program which applies the finite element method (FEM) to a linear two point boundary value problem in one spatial dimension; this code is an example for the Texas Finite Element Series, by Eric Becker, Graham Carey and J Tinsley Oden.

Licensing:

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

Languages:

FEM1D_ODEN is available in a FORTRAN77 version.

Related Data and Programs:

FEM1D, a FORTRAN77 program which applies the finite element method (FEM) to a 1D linear two point boundary value problem (BVP).

FEM1D_ADAPTIVE, a FORTRAN77 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 FORTRAN77 program which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.

FEM1D_NONLINEAR, a FORTRAN77 program which applies the finite element method to a nonlinear two point boundary value problem in a 1D region.

FEM1D_PMETHOD, a FORTRAN77 program which applies the p-method version of the finite element method to a linear two point boundary value problem in a 1D region.

FEM1D_PROJECT, a FORTRAN77 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 FORTRAN77 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. Eric Becker, Graham Carey, John Oden,
   Finite Elements, An Introduction, Volume I,
   Prentice-Hall, 1981,
   ISBN: 0133170578,
   LC: TA347.F5.B4.

Source Code:

• code1.f, the source code.
• bc_data.inc, an include file for boundary data.
• control.inc, an include file for general control data.
• elements.inc, an include file for element data.
• integration.inc, an include file for numerical integration.
• node.inc, an include file for node data.
• code1.sh, commands to compile the source code.

Examples and tests:

QUADS defines a grid of quadratic elements.

• quads_input.txt, the input file.
• quads_output.txt, the output file.
• quads_data.txt, a data file that can be read by gnuplot.
• quads_commands.txt, sample gnuplot commands.
• quads.png, a plot file created by gnuplot.

List of Routines:

• MAIN is the main program for CODE1.
• PREP does preprocessing.
• RCON reads control parameters.
• RNODE reads node information.
• RELEM reads element information.
• RMAT reads material information.
• RBC reads boundary condition information.
• PROC carries out the solution procedure.
• SETINT sets quadrature data.
• FORMKF sets the stiffness matrix and right hand side.
• ELEM integrates the equations over one element.
• SHAPE evaluates the shape functions.
• GETMAT retrieves the properties of a given material.
• ASSMB adds an elemental contribution to the global matrix.
• APLYBC applies boundary conditions.
• DRCHLT applies a Dirichlet boundary condition.
• SOLVE solves the linear system.
• TRI factors a linear system.
• BACK solves a linear system with factored matrix.
• POST carries out post-processing.
• EVAL evaluates the computed solution at a point.
• EXACT evaluates the exact solution.
• ENORMS evaluates error norms.

You can go up one level to the FORTRAN77 source codes.