27 citations · 110 across the 24 of their papers we have counts for
24 papers
Numerical methods for diffusion coefficient recovery
Sahat Pandapotan Nainggolan, Julius Fergy Tiongson Rabago, Hirofumi Notsu
We revisit the inverse problem of reconstructing a spatially varying diffusion coefficient in stationary elliptic equations from boundary Cauchy data. From a theoretical perspectiv…
Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity
Oussama Ounissi, Masato Kimura, Hirofumi Notsu
In this study, we consider a spring-block system that approximates a -dimensional linear elastic body, where or . We derive a matrix as the spring constan…
Shape optimization for piecewise parameter identification in inverse diffusion problems with a single boundary measurement
Manabu Machida, Hirofumi Notsu, Julius Fergy Tiongson Rabago
This paper proposes a unified shape and coefficient optimization approach for inverse problems governed by diffusion equations. The associated forward problem is considered with a…
Detecting immersed obstacle in Stokes fluid flow using the coupled complex boundary method
Julius Fergy Tiongson Rabago, Lekbir Afraites, Hirofumi Notsu
A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bound…
Error Estimates for First- and Second-Order Lagrange-Galerkin Moving Mesh Schemes for the One-Dimensional Convection-Diffusion Equation
Kharisma Surya Putri, Tatsuki Mizuochi, Niklas Kolbe +1
A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is pr…
Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization settings
Julius Fergy T. Rabago, Hirofumi Notsu
A new reformulation of a free boundary problem for the Stokes equations governing a viscous flow with overdetermined condition on the free boundary is proposed. The idea of the met…
A two-step Lagrange-Galerkin scheme for the shallow water equations with a transmission boundary condition and its application to the Bay of Bengal region. Part I: Flat bottom topography
Md Mamunur Rasid, Masato Kimura, Md Masum Murshed +2
This study presents a two-step Lagrange-Galerkin scheme for the shallow water equations with a transmission boundary condition (TBC). Firstly, the experimental order of convergence…
A Convective Boundary Condition for the Navier-Stokes Equations: Existence Analysis and Numerical Implementations
John Sebastian H. Simon, Hirofumi Notsu
Due to computational complexity, fluid flow problems are mostly defined on a bounded domain. Hence, capturing fluid outflow calls for imposing an appropriate condition on the bound…
Maximizing Vortex for the Navier--Stokes Flow with a Convective Boundary Condition: A Shape Design Problem
John Sebastian H. Simon, Hirofumi Notsu
In this study, a shape optimization problem for the two-dimensional stationary Navier--Stokes equations with an artificial boundary condition is considered. The fluid is assumed to…
A mass-preserving two-step Lagrange-Galerkin scheme for convection-diffusion problems
Kouta Futai, Niklas Kolbe, Hirofumi Notsu +1
A mass-preserving two-step Lagrange-Galerkin scheme of second order in time for convection-diffusion problems is presented, and convergence with optimal error estimates is proved i…
Second-order finite difference approximations of the upper-convected time derivative
Debora O. Medeiros, Hirofumi Notsu, Cassio M. Oishi
In this work, new finite difference schemes are presented for dealing with the upper-convected time derivative in the context of the generalized Lie derivative. The upper-convected…
A Shape Optimization Problem Constrained with the Stokes Equations to Address Maximization of Vortices
John Sebastian H. Simon, Hirofumi Notsu
We study an optimization problem that aims to determine the shape of an obstacle that is submerged in a fluid governed by the Stokes equations. The mentioned flow takes place in a…
Computing with vortices: Bridging fluid dynamics and its information-processing capability
Ken Goto, Kohei Nakajima, Hirofumi Notsu
Herein, the Karman vortex system is considered to be a large recurrent neural network, and the computational capability is numerically evaluated by emulating nonlinear dynamical sy…
Chaos in nanomagnet via feedback current
Tomohiro Taniguchi, Nozomi Akashi, Hirofumi Notsu +3
Nonlinear magnetization dynamics excited by spin-transfer effect with feedback current is studied both numerically and analytically. The numerical simulation of the Landau-Lifshitz…
Stability estimates and a Lagrange-Galerkin scheme for a Navier-Stokes type model of flow in non-homogeneous porous media
Imam Wijaya, Hirofumi Notsu
The purposes of this work are to study the -stability of a Navier-Stokes type model for non-stationary flow in porous media proposed by Hsu and Cheng in 1989 and to develop…
Theoretical and numerical studies for energy estimates of the shallow water equations with a transmission boundary condition
Md. Masum Murshed, Kouta Futai, Masato Kimura +1
Energy estimates of the shallow water equations (SWEs) with a transmission boundary condition are studied theoretically and numerically. In the theoretical part, using a suitable e…
Analysis of a projection method for the Stokes problem using an -Stokes approach
Masato Kimura, Kazunori Matsui, Adrian Muntean +1
We generalize pressure boundary conditions of an -Stokes problem. Our -Stokes problem connects the classical Stokes problem and the corresponding pressure…
The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme
Masato Kimura, Hirofumi Notsu, Yoshimi Tanaka +1
An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow propert…
Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part I: A nonlinear scheme
Mária Lukáčová-Medvid'ová, Hana Mizerová, Hirofumi Notsu +1
We present a nonlinear stabilized Lagrange-Galerkin scheme for the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-P…
Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme
Mária Lukáčová-Medvid'ová, Hana Mizerová, Hirofumi Notsu +1
This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the m…
Error estimates of stable and stabilized Lagrange-Galerkin schemes for natural convection problems
Hirofumi Notsu, Masahisa Tabata
Optimal error estimates of stable and stabilized Lagrange-Galerkin (LG) schemes for natural convection problems are proved under a mild condition on time increment and mesh size. T…
Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations
Hirofumi Notsu, Masahisa Tabata
Error estimates with optimal convergence orders are proved for a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a combination of Lagrange-Galerk…
A local analysis of the axi-symmetric Navier-Stokes flow near a saddle point and no-slip flat boundary
Pen-Yuan Hsu, Hirofumi Notsu, Tsuyoshi Yoneda
As one of the violent flow, tornadoes occur in many place of the world. In order to reduce human losses and material damage caused by tornadoes, there are many research methods. On…
Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type
Shuichi Jimbo, Masato Kimura, Hirofumi Notsu
We study an asymptotic behaviour of the principal eigenvalue for an elliptic operator with large advection which is given by a gradient of a potential function. It is shown that th…