A robust PetrovGalerkin discretisation of convectiondiffusion equations ?
A PetrovGalerkin discretisation is studied of an ultra-weak variational formulation of the convectiondiffusion equation in a mixed form. To arrive at an implementable method, the truly optimal test space has to be replaced by its projection onto a finite dimensional test search space. To prevent that this latter space has to be taken increasingly large for vanishing diffusion, a formulation is constructed that is well-posed in the limit case of a pure transport problem. Numerical experiments show approximations that are very close to the best approximations to the solution from the trial space, uniformly in the size of the diffusion term.
petrovgalerkin discretisation convectiondiffusion equation optimal test space