摘要：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.
其他摘要：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.
