FEM1D
Piecewise Linear Finite Element Method for 1D problem.

FEM1D is a C++ program which applies the finite element method to a linear two point boundary value problem in one spatial dimension.

Usage:

fem1d

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 of the data files that can be used to describe a finite element model.

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

FEM_50_HEAT is a MATLAB program which solves 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 C++ library which reads or writes the node, element and data files that define a finite element model.

FEM_TO_TEC is a MATLAB program which can convert an FEM model into a TEC graphics file.

FEM1D is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

FEM1D_ADAPTIVE is 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_NONLINEAR is a C++ program which applies the finite element method to a nonlinear two point boundary value problem in a 1D region.

FEM1D_PMETHOD is a C++ 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 is 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.

FEM2D_HEAT is a C++ program which solves the time dependent heat equation on the unit square.

FEM2D_POISSON is a C++ program which solves Poisson's equation on a square, using the finite element method.

FEM2D_SAMPLE is a C++ library which evaluates a finite element function defined on an order 3 or order 6 triangulation.

FEMPACK is a C++ library which is useful for finite element calculations.

PIECEWISE_LINEAR_PRODUCT_INTEGRAL is a C++ 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.C, the source code.
• fem1d.csh, commands to compile the source code.

Examples and Tests:

• fem1d_output.txt, the printed output from a run of the program.

List of Routines:

• MAIN is the main program for FEM1D.
• ASSEMBLE assembles the matrix and right-hand-side of the linear system.
• FF evaluates the right hand side function.
• GEOMETRY sets up the geometry for the interval [XL,XR].
• INIT assigns values to variables which 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.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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