A Newton type linearization based two grid method for coupling fluid flow with porous media flow

Some multilevel decoupled algorithms for a mixed navier-stokes/darcy model

“…From Lemma 4.1, we know that L = 1 (in (4.1)-(4.4) by changing H to be h 0 and h to be h 1 ), the error estimates for the intermediate-step solution, and the final-step solution hold true. For both k = 1 and k = 2, if h 1 = h 2 0 the estimates (4.24)-(4.27) hold true (see also Remark 4.1 in [26]). We are going to prove the results for a general meshlevel l. We will discuss the two cases: k = 1 and k = 2 separately.…”

“…We see that when L = 1, Algorithm A is reduced to the two-level algorithm developed in [26], Algorithm C degenerates to the two-level algorithm proposed in [35,8]. Algorithm B is an extension of the two-grid algorithm proposed in [40].…”

“…For instance, if k = 1, one can apply the Mini elements [5,22] in Ω f and the piecewise linear elements in Ω p . If k ≥ 2, the k-th order Taylor-Hood elements [5,22,39] and P k elements can be applied in Ω f and Ω p respectively [5,7,26]. For simplicity, we will only consider the cases k = 1 and k = 2 for numerical experiments in this paper.…”

“…These multilevel algorithms are extended from the existing two-level algorithms [26,8,35,15,24,41,29,30,44]. However, the error estimates of the multilevel algorithms are much more difficult than those of two-level algorithms.…”

“…The first multi-level algorithm is actually an extension of the two-level algorithm developed in [26]. After solving the nonlinear coupled problem on a coarse grid level (cf.…”