FEM1D_ADAPTIVE
Finite Element Method with Adaptive Refinement

FEM1D_ADAPTIVE is a FORTRAN90 program which applies the finite element method to a linear two point boundary value problem in one spatial dimension, using adaptive refinement to estimate the error, refine the mesh, and produce an improved solution.

Usage:

fem1d_adaptive

runs the program.

Licensing:

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

Related Data and Programs:

FEM is a data directory which contains a description and examples of files that describe a finite element model.

FEM_50 is a MATLAB program which implements a finite element calculation in just 50 lines of code.

FEM_50_HEAT is a MATLAB program which implements a finite element calculation specifically for the heat equation.

FEM_BASIS_T3_DISPLAY is a MATLAB program which displays a basis function associated with a linear triangle ("T3") mesh.

FEM_BASIS_T6_DISPLAY is a MATLAB program which displays a basis function associated with a quadratic triangle ("T6") mesh.

FEM_IO is a FORTRAN90 library which reads or writes node, element and data files defining a finite element model.

FEM_TO_TEC is a FORTRAN90 program which converts FEM models into TEC graphics files.

FEM1D is a FORTRAN90 program which applies the finite element method to a 1D linear two point boundary value problem.

FEM1D_ADAPTIVE is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

FEM1D_NONLINEAR is a FORTRAN90 program which applies the finite element method to a 1D nonlinear two point boundary value problem.

FEM1D_PMETHOD is a FORTRAN90 program which applies the p-method version of the finite element method to a 1D linear two point boundary value problem.

FEM1D_PROJECT is a FORTRAN90 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 FORTRAN90 program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.

FEM2D_HEAT is a FORTRAN90 program which solves the 2D time dependent heat equation on the unit square.

FEM2D_POISSON is a FORTRAN90 program which solves the 2D Poisson equation on a square, using the finite element method.

PIECEWISE_LINEAR_PRODUCT_INTEGRAL is a FORTRAN90 library which calculates the exact value of the integral of the product of two piecewise linear functions F(X) and G(X).

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_adaptive.f90, the source code.
• fem1d_adaptive.csh, commands to compile the source code.

Examples and Tests:

• fem1d_adaptive_output.txt, the output file.

List of Routines:

• MAIN is the main program for FEM1D_ADAPTIVE.
• ASSEMBLE assembles the global matrix.
• FF evaluates the function F in the differential equation.
• GEOMETRY sets up some of the geometric information for the problem.
• GETBETA returns the value of BETA, for use by problem 5.
• GETEPS returns the value of EPS, for use by problem 6.
• GETPRB returns the value of the current problem number.
• INIT initializes some parameters that define the problem.
• OUTPUT prints out the computed solution.
• PHI evaluates a linear basis function and its derivative.
• PP evaluates the function P in the differential equation:
• PRSYS prints out the tridiagonal linear system.
• QQ evaluates the function Q in the differential equation.
• SOLVE solves a tridiagonal matrix system of the form A*x = b.
• SOLVEX discretizes and solves a differential equation given the nodes.
• SOLVEY computes error estimators for a finite element solution.
• SUBDIV decides which intervals should be subdivided.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UEXACT returns the value of the exact solution at any point X.

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