M. Stynes, On Faster Convergence of the Bisection Method for all Triangles, Mathematics of Computation, Vol. 35, Number 152, October 1980, pp. 1195-1202.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....dimensions, an element is refined by bisecting its longest edge (two triangle algorithm) 59] Elements with non conforming edges are subdivided following the patterns of Figure 44. The process terminates in a finite number of steps. Following the results of Rosenberg and Stenger [61] and Stynes [82] about longest edge bisection, the scheme is stable, furthermore, interior angles are always greater than one half of the lowest angle in the initial triangulation ,S2 [59] I non conf. vert. 2 non conf. vert. Non conforming vertex on face s Longest edge 3 non conf. vert. Figure 44. ....

....edges in a recursive fashion. Unlike the two dimensional case, an element that needs refinement or is non confoming must be bisected at its longest edge. This scheme guarantees nesting. In two dimensions, following the longest edge bisection results of Rosenberg and Stenger [61] and Stynes [82], the scheme is stable, furthermore, interior angles are always greater than one half of the lowest angle in the initial triangulation ,S2 [59] In three dimensions, to this point in time, no one has yet presented a proof of the stability of the scheme probably because (i) the longest edge in a ....

M. Stynes. On faster convergence of the bisection method for all triangles. Math. of Computation, 35(152):1195-1201, October 1980.

....bisected across their longest edges, the smallest resulting angle is bounded by at worst one half the smallest angle in the original triangle [33] A simple corollary is that the largest resulting angle is also bounded away from . Moreover, the angles of M k tend to go toward 3 as k 1 [35]. X Fig. 8. Triangle X on the left has been bisected into two triangles. At this stage the resulting triangulation is nonconforming. A third means of triangle division is regular refinement [4] as illustrated in Figure 9. Again, this approach can result in a nonconforming mesh, as shown on the ....

M. Stynes, On faster convergence of the bisection method for all triangles, Mathematics of Computation, 35 (1980), pp. 1195--1201.

....2 Fig. 6: Newest Vertex Bisection The second approach, due to Rivara, is based on using the triangle s longest edge for refinement, 22] The stability of this method follows from the fact that longest edge bisection changes into newest vertex bisection after a finite number of refinement steps, [24]. Hence, the number of congruence classes is also finite but in general it depends on ffi(T 0 ) Consistency is achieved by a recursive process similar to the one of Mitchell. Rivara s method applies to any consistent triangulation. In contrast to newest vertex bisection, it is not affine ....

M. Stynes, On faster convergence of the bisection method for all triangles, Math. Comp., 35 (1980), pp. 1195--1201.

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M. Stynes, On Faster Convergence of the Bisection Method for all Triangles, Mathematics of Computation, Vol. 35, Number 152, October 1980, pp. 1195-1202.

No context found.

M. Stynes, On faster convergence of the bisection method for all triangles, Math. Comp. 35 (1980), 1195--1201.

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M. Stynes. On faster convergence of the bisection method for all triangles. Math. Comp. 35(152):1195--1201, 1980.

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