This is confirmed by assuring that the calculation results are independent with respect to grid refinement.
Some works can be found in the literature with respect to query refinement in DLs as in [2, 3].
It is important to observe that the effectivity upper bounds, (48) and (49), are independent of N, and hence stable with respect to RB refinement.
The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size).
In contrast with the original hybrid method, the new hybrid algorithm is very robust with respect to grid refinement and achieves grid convergence without any unphysical vortex shedding in the cold bluff-body flow case.
Lemma 10.6 Suppose that (μ, v ) ≔ (λ (T ), u (T ) ) ∈ X (T ) and (μ ^, v ^ ) ≔ (λ (T ^ ), u (T ^ ) ) ∈ X (T ^ ) denote the discrete Eigenpairs with respect to some refinement T ^ ∈ T of T ∈ T and let (λ, u ) denote the exact Eigenpair.
For a given polynomial order p, all multigrid cycles are of optimal complexity with respect to the mesh refinement.
For all polynomial orders, all the approaches exhibit optimal convergence with respect to the mesh refinement, which confirm the theoretical estimates (41) for two-grid method, and (64)–(66) for multigrid methods.
The general problem we address is the following: Given a non-binary gene tree G and a species tree S, find a refinement of G containing the minimum number of NADs with respect to S. Such a refinement of G is called a minimum refinement of G w.r.t. S. Hence, we aim at refining each non-binary node of G.
This paper presents an original formulation to define a tension stiffening diagram that reduces the dependency of the results with respect to the adopted mesh refinement in structures in which crack propagation is governed by mode I (crack opening).
