Robust Computational Techniques for Boundary Layers

By P. Farrell, A. Hegarty, JohnM . Miller, Eugene O'Riordan, G. Shishkin. 2000

896 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Singularly perturbed parabolic problems with non-smooth data (2004, methodology): “A ;tted mesh method for problems from the above class is now introduced (see [3] for motivation for this choice of mesh).”
A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection-diffusion problem (2008, background): “a(x) > 0 and b(x) 0, such that, the boundary layer is located at x = 1 and condition b(x) 0 ensures the uniqueness of the solution (see [9,3,13]).”
A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems (2003, neutral): “To compute the rate of convergence of the numerical method, we follow the practice suggested in Chapter 8 of Farrell et al. (2000) by computing the two-mesh differenceDNε,µ = ‖ U N − U2Nh ‖Ω N and the parameter-uniform two-mesh errorDN := maxε,µ{DNε,µ}, whereε andµ take the values 1, 10−1, 10−2, .…”
Singularly perturbed convection-diffusion problems with boundary and weak interior layers (2004, background): “Lemma 3 [1] For each integer k, satisfying 0 ≤ k ≤ 3, the solution w1 of (2.”
Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers (2003, neutral): “For more details about the numerical methods, the readers may refer to the books of Miller et al. [8], Roos et al. [14] and Farrell et al. [5].”