Discontinuous Mixed Space-Time Least-Squares Formulation for Transient Advection-Diffusion-Reaction Equations

Abstract

In a previous work we proposed a constant discontinuous space-time
least-squares finite element formulation, where a -averaged scheme was
used to consider distinct time discretizations and a von Neumann
stability analysis displayed, for 0.5 unconditionally stable solutions
for any Courant num- ber for 1-D problems. Optimal convergence results
were obtained for = 0.5 and Courant number equal one. In this work we
present mixed discontinuous space-time least-square finite element
formulations applied for advection-diffusion-reaction equation,
resolved into first order system of differential equation
approximating both the prime field variable and its fluxes through a -
averaged scheme to allow distinct time discretizations. We also
present coercivity proof of the bilinear form for this problem,
together with its error estimates and show that this formulation is
not subjected to LBB condition.