Most widely held works by Norikazu Saito
Operator theory and numerical methods by Hiroshi Fujita ( Book )
15 editions published between 2001 and 2006 in English and held by 305 WorldCat member libraries worldwide
In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method
Suchi kaiseki nyumon by Norikazu Saito ( Book )
2 editions published in 2012 in Japanese and held by 4 WorldCat member libraries worldwide
Remarks on traces of H¹-functions defined in a domain with corners by Norikazu Saito ( Book )
1 edition published in 1999 in English and held by 3 WorldCat member libraries worldwide
Abstract: "The set of traces of H¹ ([omega])-functions on a part [gamma] of the boundary [curly d][omega] is considered, where [omega] is a bounded domain in R² with a certain singularity, particularly, with corners at the end points of [gamma]. The aim of the present paper is to show that the set of all traces of functions in H¹([omega]) is equal algebraically and topologically to the domain of a certain fractional power of minus Laplacian on [gamma] with the zero boundary condition. The result is expected to be of use for the mathematical analysis of the DDM (domain decomposition method) applied to such [omega]."
On the domain-dependence of convergence rate in a domain decomposition method for the Stokes equations by Norikazu Saito ( Book )
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
Abstract: "A certain domain decomposition iterative algorithm for the Stokes equations is considered. The aim of the present paper is to study relationships between the convergence speed of iteration and the shapes of subdomains. Our consideration is restricted to the continuous problem and to the case in which the whole domain is divided into two non-overlapping subdomains. Then, introducing a certain geometric condition, we can derive explicit decay rates of the error on an artificial boundary. Also, a new important role of the so-called inf-sup constant is revealed. The proof is accomplished by means of an operator theory."
Regularity of solutions to the Stokes equations under a certain nonlinear boundary condition by Norikazu Saito ( Book )
1 edition published in 2000 in English and held by 2 WorldCat member libraries worldwide
Abstract: "The regularity of a solution to the variational inequality for the Stokes equation is considered. The inequality describes the steady motion of the viscous incompressible fluid under a certain unilateral constrain of friction type. Firstly the solution is approximated by solutions to a regularized problem which is introduced by Yosida's regularization for a multi-valued opearator [sic]. Then we establish a regularity result to the regularized problem. The regularity of the solution to the original inequality follows by the limiting argument."
Sūchi-kaiseki-ni-okeru-riron, shuhō, ōyō : RIMS-kenkyū-shūkai-hōkokushū ; Kyōto, November 12 - 14, 2008 = Numerical analysis: theory, methods and applications ( Book )
1 edition published in 2009 in Japanese and held by 2 WorldCat member libraries worldwide
Saito, Norikazu, 1971-
サイトウ, ノリカズ, 1971-