A Modification of the Petrov-Galerkin Method for the Transient Convection-Diffusion Equation
A variation of the Petrov–Galerkin method of solution of a partial differential equation is presented in which the weight function applied to the time derivative term of the transient convection–diffusion equation is different from the weight function applied to the special derivatives. This allows for the formulation of fourth-order explicit and centred difference schemes. Comparison with analytic solutions show that these methods are able to capture steep wave fronts. The ability of the explicit method to capture wave fronts increases as the amount of convective transport increases.
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Cardle, J. A.
A Modification of the Petrov-Galerkin Method for the Transient Convection-Diffusion Equation.
International Journal for Numerical Methods in Engineering, 38(2),