We study here some linear elliptic partial differential equations (with Dirichlet, Fourier or mixed boundary conditions), to which convection terms (first order perturbations) are added that entail the loss of the classical coercivity property. We prove the existence, uniqueness and regularity results for the solutions to these problems. Mathematics Subject Classification (2000): 35J25.

We consider a convection–diffusion–reaction problem, and we analyze a stabilized mixed finite volume scheme introduced in [23]. The scheme is presented in the format of Discontinuous Galerkin methods, and error bounds are given, proving O(h1/2) convergence in the L2-norm for the scalar variable, which is approximated with piecewise constant elements.

We present a convergence analysis of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-diiusion problems. The scheme is unconditionally stable, independent of the diiusion coeecient, even in the case when numerical quadrature is used. The theoretical predictions are illustrated by a series of numerical experiments. For the periodic case, our results present a sign...