In this paper, we discuss the convergence properties of the memoryless quasi-Newton method proposed by Shanno (1978). In the two-dimensional quadratic case, we prove the global convergence of the method without any li...
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In this paper, we discuss the convergence properties of the memoryless quasi-Newton method proposed by Shanno (1978). In the two-dimensional quadratic case, we prove the global convergence of the method without any line search; if an exact line search is made at the first iteration, then the method gives the exact solution at most at the forth iteration. Numerical experiments further demonstrate these properties of the memoryless quasi-Newton method.
A new finite volume scheme, based on first order monotone scheme and limited linear reconstruction, is constructed for scalar hyperbolic conservation laws in two dimension,the scheme satisfies the maximum principle an...
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A new finite volume scheme, based on first order monotone scheme and limited linear reconstruction, is constructed for scalar hyperbolic conservation laws in two dimension,the scheme satisfies the maximum principle and approximation the flux with second order accuracy. Numerical results for constant coefficient linear advection and Burgers’equation are presented.
In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using...
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In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using a conforming interpolation operator and construct a uniformly bounded decomposition for the finite element space. Both coarse and fine grid spaces are nonconforming. We get optimal convergence properties of the additive Schwarz algorithm that is constructed on nonnested meshes and with a not necessarily shape regular subdomain partitioning. Our analysis is based on the theory of Dryja and *** is interesting to mention that when coarse and fine spaces are all nonconforming, a natural intergrid operator seems to be one defined by taking averages of the nodal parameters. In this way, we obtain the stable factor (H/h)3/2, and show that this factor can not be improved. However, to get an optimal preconditioner,we need in general the stability with a factor C independent of mesh ***. the latter can not be used in this case.
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