90 citations · 251 across the 30 of their papers we have counts for
32 papers
Local-in-time strong solvability of Navier--Stokes type variational inequalities by Rothe's method
Takahito Kashiwabara
We consider parabolic variational inequalities in a Hilbert space , which have a non-monotone nonlinearity of Navier--Stokes type represented by a bilinear operator $B: V \times…
Single exponential -upper bounds for the primitive equations
Takahito Kashiwabara
The three dimensional primitive equations with full viscosity are considered in a horizontally periodic box , which are subject to either the homogeneous Neumann or Dirichlet co…
Optimal -error estimate for isoparametric finite element method in a smooth domain
Takahito Kashiwabara
We consider the isoparametric finite element method (FEM) for the Poisson equation in a smooth domain with the homogeneous Dirichlet boundary condition. Because the boundary is cur…
On periodic traveling wave solutions with or without phase transition to the Navier-Stokes-Korteweg and the Euler-Korteweg equations
Yoshikazu Giga, Takahito Kashiwabara, Haruki Takemura
The Navier-Stokes-Korteweg and the Euler-Korteweg equations are considered in isothermal setting. These are diffuse interface models of two-phase flow. For the Navier-Stokes-Kortew…
The well-posedness and regularity of the Non-stationary Stokes and Navier-Stokes equations with the friction-type interface condition
Qi Wang, Takahito Kashiwabara, Guanyu Zhou
The friction-type interface condition (FIC) is introduced to describe the phenomenon of the slip and leak of fluid flow on the interface happens only when the difference of stress…
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…
-regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition
Takeshi Fukao, Takahito Kashiwabara
-spatial regularity of stationary and non-stationary problems for Bingham fluids formulated with the pseudo-stress tensor is discussed. The problem is mathematically described…
Error estimates of the cubic interpolated pseudo-particle scheme for one-dimensional advection equations
Takahito Kashiwabara, Haruki Takemura
Error estimates of cubic interpolated pseudo-particle scheme (CIP scheme) for the one-dimensional advection equation with periodic boundary conditions are presented. The CIP scheme…
The three limits of the hydrostatic approximation
Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3
The primitive equations are derived from the -Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an -thin domain and anisotropic viscosit…
Finite element analysis of a generalized Robin boundary value problem in curved domains based on the extension method
Takahito Kashiwabara
A theoretical analysis of the finite element method for a generalized Robin boundary value problem, which involves a second-order differential operator on the boundary, is presente…
Discrete maximal regularity for the discontinuous Galerkin time-stepping method without logarithmic factor
Takahito Kashiwabara, Tomoya Kemmochi
Maximal regularity is a kind of a priori estimates for parabolic-type equations and it plays an important role in the theory of nonlinear differential equations. The aim of this pa…
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…
Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized elastodynamic body
Hiromichi Itou, Takahito Kashiwabara
We consider dynamic motion of a linearized elastic body with a crack subject to a modified contact law, which we call the Signorini contact condition of dynamic type, and to the Tr…
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.…
Justification of the Hydrostatic Approximation of the Primitive Equations in Anisotropic Space $L^\infty_H L^q_{x_3}(\Torus^3)$
Ken Furukawa, Takahito Kashiwabara
The primitive equations are fundamental models in geophysical fluid dynamics and derived from the scaled Navier-Stokes equations. In the primitive equations, the evolution equation…
A robust discontinuous Galerkin scheme on anisotropic meshes
Takahito Kashiwabara, Takuya Tsuchiya
Discontinuous Galerkin (DG) methods are extensions of the usual Galerkin finite element methods. Although there are vast amount of studies on DG methods, most of them have assumed…
The Hydrostatic Approximation for the Primitive Equations by the Scaled Navier-Stokes Equations under the No-Slip Boundary Condition
Ken Furukawa, Yoshikazu Giga, Takahito Kashiwabara
In this paper we justify the hydrostatic approximation of the primitive equations in the maximal --setting in the three-dimensional layer domain $Ω= \Torus^2 \times (-1,…
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…
Penalty method with Crouzeix-Raviart approximation for the Stokes equations under slip boundary condition
Takahito Kashiwabara, Issei Oikawa, Guanyu Zhou
The Stokes equations subject to non-homogeneous slip boundary conditions are considered in a smooth domain . We propose a finite element scheme bas…
Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations
Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3
Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equat…
Maximum norm error estimates for the finite element approximation of parabolic problems on smooth domains
Takahito Kashiwabara, Tomoya Kemmochi
In this paper, we consider the finite element approximation for a parabolic problem on a smooth domain with the inhomogeneous Neumann boundary condition. We…
- and -error estimates of linear finite element method for Neumann boundary value problems in a smooth domain
Takahito Kashiwabara, Tomoya Kemmochi
Pointwise error analysis of the linear finite element approximation for in , on , where is a bounded smooth domain in $\mathbb R^…
The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions
Yoshikazu Giga, Mathis Gries, Matthias Hieber +2
Consider the -d primitive equations in a layer domain , , subject to mixed Dirichlet and Neumann boundary conditions at and , respectiv…
Analyticity of solutions to the primitive equations
Yoshikazu Giga, Mathis Gries, Matthias Hieber +2
This article presents the maximal regularity approach to the primitive equations. It is proved that the primitive equations on cylindrical domains admit a unique, global stron…