The "UNSTEADY_CONVECTION_DIFFUSION" script solves the 2D scalar equation of a convection-diffusion problem with bilinear quadrangular elements.
The space discretization is performed by means of the standard Galerkin 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 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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Andrea La Spina (2020). 2D Unsteady convection-diffusion problem (https://www.mathworks.com/matlabcentral/fileexchange/60867-2d-unsteady-convection-diffusion-problem), MATLAB Central File Exchange. Retrieved .