Convergence of a Ramshaw-Mesina iteration
Applied Mathematics Letters(2024)
摘要
In 1991 Ramshaw and Mesina introduced a clever synthesis of penalty methods and artificial compression methods. Its form makes it an interesting option to replace the pressure update in the Uzawa iteration. The result, for the Stokes problem, is (1)Step1:−△un+1+∇pn=f(x),inΩ,un+1|∂Ω=0,Step2:pn+1−pn+β∇⋅(un+1−un)+α2∇⋅un+1=0.For saddle point problems, including Stokes, this iteration converges under a condition similar to the one required for Uzawa iteration.
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关键词
Uzawa iteration,Saddle point problem,Penalty,Artificial compression
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