HEAT_ONED
Finite Element Solution of the
Time Dependent 1D Heat Equation
using Implicit Time Stepping


HEAT_ONED is a MATLAB program which solves the time-dependent 1D heat equation, using the finite element method in space, and the backward Euler method in time, by Jeff Borggaard.

The procedure discretizes space using the finite element method, and solves the time dependence with the method of lines, using the backward Euler method to approximate the time derivative.

This program solves

        dUdT - k * d2UdX2 = F(X,T)
      
over the interval [A,B] with boundary conditions
        U(A,T) = UA(T),
        U(B,T) = UB(T),
      
over the time interval [T0,T1] with initial conditions
        U(X,T0) = U0(X)
      

The spatial derivatives are approximated using the finite element method, with piecewise linear or quadratic elements.

The solver applies an implicit backward Euler approximation to the first derivative in time.

Licensing:

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

Languages:

HEAT_ONED is available in a MATLAB version.

Related Data and Programs:

FD1D_HEAT_IMPLICIT, a MATLAB library which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.

FD1D_HEAT_STEADY, a MATLAB program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.

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

Author:

Jeff Borggaard

Source Code:

Examples and Tests:

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


Last revised on 21 December 2012.