FEM_NEUMANN
1D Time-Dependent Reaction-Diffusion Equation
Neumann Boundary Conditions
Finite Element Method

FEM_NEUMANN is a MATLAB program which sets up a time-dependent reaction-diffusion equation in 1D, with Neumann boundary conditions, discretized using the finite element method, by Eugene Cliff.

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:

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

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

FEM1D_BVP_LINEAR, a MATLAB 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 MATLAB program which applies the finite element method to a 1D nonlinear two point boundary value problem.

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

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

Author:

Eugene Cliff

Reference:

1. Jeffrey Borggaard, John Burkardt, John Burns, Eugene Cliff,
   Working Notes on a Reaction Diffusion Model: a Finite Element Formulation.

Source Code:

• basic_hat.m, evaluates the basic hat function on [-1, 1].
• plot_rd.m, makes two plots of the reaction-diffusion solution.
• rd_fem.m, solves a 1D reaction/diffusion problem using finite elements.
• rd_lin_spline.m, discretizes and solves a 1D reaction diffusion problem.
• timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• solution.png, a surface plot of W(T,X).
• solution_norm.png, a plot of the time-evolution of the spatial L2 norm of W(T,*).

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