8 papers
Stable Reduction of Unresolved Dynamics: An Operator-Theoretic Framework
Hiroki Ishizaka
Dimension reduction removes variables, but a reliable reduction should not erase their dynamical influence. We study this principle for linear block evolution systems on resolved a…
Graph-space well-posedness for diffusion equations with degenerate instantaneous diffusion
Hiroki Ishizaka
We study diffusion equations with completely monotone memory when the instantaneous diffusion form is merely non-negative and may therefore lose coercivity. For a kernel whose Bern…
High-frequency coercivity loss for completely monotone memory on bounded time intervals
Hiroki Ishizaka
We study Volterra memory terms with locally integrable completely monotone kernels on a finite time interval $(0,\Tend)$ and ask how much coercivity they retain at high tem…
Weighted well-posedness and kernel stability for coercive evolution equations with measure-valued delays
Hiroki Ishizaka
We consider coercive evolution equations with measure-valued delay on a Gelfand triple. The delayed feedback is induced by a bounded form on and may contain principal spatial d…
Low-order CR--RT equilibrated-flux certification for semilinear problems on anisotropic meshes
Hiroki Ishizaka
We develop a low-order Crouzeix--Raviart--Raviart--Thomas (CR--RT) equilibrated-flux certification workflow for finite element approximations of semilinear diffusion--reaction prob…
Nitsche's method under a semi-regular mesh condition
Hiroki Ishizaka
Nitsche's method is a numerical approach that weakly enforces boundary conditions for partial differential equations. In recent years, Nitsche's method has experienced a revival ow…
Hybrid weakly over-penalised symmetric interior penalty method on anisotropic meshes
Hiroki Ishizaka
In this study, we investigate a hybrid-type anisotropic weakly over-penalised symmetric interior penalty method for the Poisson equation on convex domains. Compared with the well-k…
Note on a weakly over-penalised symmetric interior penalty method on anisotropic meshes for the Poisson equation, Ver. 1
Hiroki Ishizaka
The purpose is to make an easy-to-understand note of "Special Topics in Finite Element Methods." There might be typos and mistakes. Therefore, I do not take any responsibility for…