Unsteady convection-diffusion-reaction problem

1D scalar equation of a convection-diffusion-reaction problem with piecewise linear approximation

The "UNSTEADY_CONVECTION_DIFFUSION_REACTION_1D" script solves the 1D scalar equation of a convection-diffusion-reaction problem with piecewise linear approximation.

For the space discretization the user can choose the standard Galerkin or the Full Upwind approach.

For the time integration the theta-method has been implemented. According to the value of theta these schemes are obtained:

0 -> Forward Euler

1/2 -> Crank-Nicolson

3/4 -> Galerkin

1 -> Backward Euler

The FEM parameters such as the number of finite elements and the number of Gauss integration points can be easily chosen.

The the boundary conditions can be expressed a function of time and a nonlinear source term s(x) can be taken into account.

The functions and the examples are developed according with Chapter 5 "Unsteady convection-diffusion

problems" of the book "Finite Element Methods for flow problems" of Jean Donea and Antonio Huerta.

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