RATE OF CONVERGENCE OF SCHWARZ ALTERNATING METHOD FOR TIME-DEPENDENT CONVECTION-DIFFUSION PROBLEM

【摘要】 <正>This paper provides a theoretical justification to a overlapping domain decomposition method applied to the solution of time-dependent convection-diffusion problems. The method is based on the partial upwind finite element scheme and the discrete strong maximum principle for steady problem. An error estimate in L∞(0, T; L∞ (Ω)) is obtained and the fact that convergence factor ρ(τ, h) →0 exponentially as τ, h→0 is also proved under some usual conditions.更多还原

【Abstract】 This paper provides a theoretical justification to a overlapping domain decomposition method applied to the solution of time-dependent convection-diffusion problems. The method is based on the partial upwind finite element scheme and the discrete strong maximum principle for steady problem. An error estimate in L∞(0, T; L∞ (Ω)) is obtained and the fact that convergence factor ρ(τ, h) →0 exponentially as τ, h→0 is also proved under some usual conditions.更多还原