Journal of the Mathematical Society of Japan 68(4) 1389-1419 Oct 2016 [Refereed]

The Green function of the Laplacian with the homogeneous Dirichlet boundary condition on bounded domains is considered. The variation of the Green function with respect to domain perturbations is called the Hadamard variation. In this paper, we pr...

We describe a technique to improve Smith's branch-and-bound algorithm for the
Euclidean Steiner tree problem in Rd. The algorithm relies on the enumeration
and optimization of full Steiner topologies for corresponding subsets of
regular points. We...

International Conference on Mathematical and Computational Methods in Science and Engineering - Proceedings 114-121 Dec 2010

Suppose that we deal with quantities defined on a domain. If the domain is perturbed, the quantities are also perturbed. Such a variation with respect to domain perturbation is called Hadamard's variation. In this paper, the authors present an ite...

In this paper, we present a scheme of convergence analysis of trial free boundary methods for the two-dimensional filtration (or dam) problem. For the purpose we present a new variational principle of the filtration problem. This variational princ...

We have found “the circumradius condition” for linear interpolation on triangular elements. We proved it without using validated numerical computation. We then found that the circumradius condition is closely related to the definition of surface a...

Suppose that we are interested in an elliptic boundary value problem defined on a bounded domain. In this research, we consider effects of perturbation of the domain to the solution of the boundary value problem. In particular, we have established...

1. We have studied on the free boundary problem called the filtration problem or the dam problem. In any cases, some level-set approaches are taken to analyze the dam problem theoretically. However, to compute the numerical solutions, iterative sc...

In this research project, we have tried to develop a mathematical theory of error analysis of finite element methods, and have obtained the following results.(1)We have consider on error analysis of Galerkin methods applied to (non-) linear equati...

In this research project, we have tried to develop an error analysis of Ritz finite element methods, and have obtained the following results.We have considered finite element approximations of conformal mappings from the unit disk to Jordan domain...