Formulação de mínimos quadrados espaço-tempo descontínuo aplicada à equação de transporte - Novo, Carolina Cardoso (2009)
The modelling of many physical engineering problems concerns solution of transport equations. Several approximations have been proposed in order to solve these equations, for example, approximations by finite differences, finite volume and finite elements, both for the semi-discrete ones as well for the approximations by finite elements in space and in time. Within this metodology of space-time finite elements, we can highlight the variational formulations that use approximations functions which are continuous in space and discontinuous in time domain. In the present work, we apply the finite elements with the discontinuous space-time least squares method to advection-diffusion and advection-diffusion-reaction problems. To solve these transport equations, we consider an equivalent system of first order differential equations. Mathematical analysis of stability and error estimative are carried for the presented mixed formulations. We also show that, even this problem is a mixed one, there is no need on satisfying the Ladyzhenskaya-Babuska-Brezzi(LBB) condition. Numerical results are presented to confirm the result achieved by the mathematical analysis here developed.