90 citations · 251 across the 30 of their papers we have counts for
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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…
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…
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…
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…
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…
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…
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^…
Penalty method with P1/P1 finite element approximation for the Stokes equations under slip boundary condition
Takahito Kashiwabara, Issei Oikawa, Guanyu Zhou
We consider the P1/P1 or P1b/P1 finite element approximations to the Stokes equations in a bounded smooth domain subject to the slip boundary condition. A penalty method is applied…
On a finite element approximation of the Stokes problem under leak or slip boundary conditions of friction type
Takahito Kashiwabara
A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary condition of friction type, is considered. We…