A posteriori error estimates for the generalized Schwarz method of a new class of advection‐diffusion equation with mixed boundary condition

Abstract

In this paper, a posteriori error estimates for the generalized Schwarz method with mixed boundary condition on the interfaces for advection‐diffusion equation with second‐order boundary value problems are proved using theta time scheme combined with Galerkin spatial method. Furthermore, a asymptotic behavior in Sobolev norm is deduced using Benssoussan‐Lions' algorithm.

Convergence Analysis of Waveform Relaxation Method to Compute Coupled Advection-Diffusion-Reaction Equations

“…Here ω min and ω max may be determined as π/T and π/∆t, with T and ∆t being the time length of problem (15) and the small time scale to be resolved, respectively. With the above procedure, the optimal value α * is estimated, and the corresponding |ρ| for Case 1 and 2 is plotted in Fig.…”

“…In the computation, the iteration can be handled by methods for elliptic equations (e.g., [13]). Studies on the conventional method include preconditioners [13], algorithms [14], error estimate [15], and convergence analysis [16]. An interesting result is that an optimal transmission algorithm leads to 'perfect convergence', referring to convergence within two times of iteration, and convergence speedup largely remains true in nonlinear situations [16].…”