4 citations · 17 across the 15 of their papers we have counts for
15 papers
An Uncertainty-aware, Mesh-free Numerical Method for Kolmogorov PDEs
Daisuke Inoue, Yuji Ito, Takahito Kashiwabara +2
This study introduces an uncertainty-aware, mesh-free numerical method for solving Kolmogorov PDEs. In the proposed method, we use Gaussian process regression (GPR) to smoothly int…
Convergence Analysis of an Upwind Finite-Difference Scheme for Hamilton-Jacobi-Bellman Equations
Daisuke Inoue, Nao Hamamuki, Yuji Ito +3
We study the convergence of an upwind finite-difference scheme for Hamilton-Jacobi-Bellman equations on a one-dimensional periodic domain, considering both the value function and t…
A fictitious-play finite-difference method for linearly solvable mean field games
Daisuke Inoue, Yuji Ito, Takahito Kashiwabara +2
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms.…
A finite element method to a periodic steady-state problem for an electromagnetic field system using the space-time finite element exterior calculus
Masaru Miyashita, Norikazu Saito
This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the…
A mass-lumping finite element method for radially symmetric solution of a multidimensional semilinear heat equation with blow-up
Toru Nakanishi, Norikazu Saito
This study presents a new mass-lumping finite element method for computing the radially symmetric solution of a semilinear heat equation in an dimensional ball (). We p…
Model Predictive Mean Field Games for Controlling Multi-Agent Systems
Daisuke Inoue, Yuji Ito, Takahito Kashiwabara +2
When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), whi…
Nitsche's method for a Robin boundary value problem in a smooth domain
Yuki Chiba, Norikazu Saito
We prove several optimal-order error estimates for a finite-element method applied to an inhomogeneous Robin boundary value problem (BVP) for the Poisson equation defined in a smoo…
Finite element method for radially symmetric solution of a multidimensional semilinear heat equation
Toru Nakanishi, Norikazu Saito
This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinear heat equations. In parti…
Weak discrete maximum principle and analysis of the DG method for the Poisson equation on a polygonal domain
Yuki Chiba, Norikazu Saito
We derive several error estimates for the symmetric interior penalty (SIP) discontinuous Galerkin (DG) method applied to the Poisson equation in a two-dimensional polygo…
The inf-sup condition and error estimates of the Nitsche method for evolutionary diffusion-advection-reaction equations
Yuki Ueda, Norikazu Saito
The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and converg…
Notes on the Banach-Necas-Babuska theorem and Kato's minimum modulus of operators
Norikazu Saito
This note was prepared for a lecture given at Kyoto University (RIMS Workshop: "The State of the Art in Numerical Analysis: Theory, Methods, and Applications", November 8-10, 2017)…
Variational analysis of the discontinuous Galerkin time-stepping method for parabolic equations
Norikazu Saito
The discontinuous Galerkin (DG) time-stepping method applied to abstract evolution equation of parabolic type is studied using a variational approach. We establish the inf-sup cond…
Hybridized discontinuous Galerkin method for elliptic interface problems
Masasru Miyashita, Norikazu Saito
New hybridized discontinuous Galerkin (HDG) methods for the interface problem for elliptic equations are proposed. Unknown functions of our schemes are in elements and $\hat{…
Convergence of the immersed-boundary finite-element method for the Stokes problem
Norikazu Saito, Yoshiki Sugitani
Convergence results for the immersed boundary method applied to a model Stokes problem with the homogeneous Dirichlet boundary condition are presented. As a discretization method,…
Discrete maximal regularity and the finite element method for parabolic equations
Tomoya Kemmochi, Norikazu Saito
Maximal regularity is a fundamental concept in the theory of partial differential equations. In this paper, we establish a fully discrete version of maximal regularity for a parabo…