9 citations · 9 across the 10 of their papers we have counts for
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Crouzeix--Raviart--Marini realisation of computable a priori -error bounds on anisotropic meshes
Hiroki Ishizaka
We consider conforming $\Pone$ and lowest-order Crouzeix--Raviart (CR) approximations of the Dirichlet Poisson problem in two and three dimensions. We obtain computable a priori $L…
Exact characterisation of maximum-angle conditions for spherical finite element meshes
Hiroki Ishizaka
Maximum-angle conditions are standard finite-element mesh hypotheses that permit anisotropic triangles excluded by minimum-angle or shape-regularity assumptions. For exact spherica…
Anisotropic modified Crouzeix-Raviart finite element method for the stationary Navier-Stokes equation
Hiroki Ishizaka
We studied an anisotropic modified Crouzeix--Raviart finite element method for the rotational form of a stationary incompressible Navier--Stokes equation with large irrotational bo…
Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition
Hiroki Ishizaka
In this study, we present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not i…
Anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation
Hiroki Ishizaka
In this study, we investigate an anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation {on convex domains}. Our approach is a simple discontin…
Anisotropic Raviart-Thomas interpolation error estimates using a new geometric parameter
Hiroki Ishizaka
We present precise Raviart-Thomas interpolation error estimates on anisotropic meshes. The novel aspect of our theory is the introduction of a new geometric parameter of simplices.…
Anisotropic interpolation error estimates using a new geometric parameter
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theo…
A new geometric condition equivalent to the maximum angle condition for tetrahedrons
Hiroki Ishizaka, Kenta Kobayashi, Ryo Suzuki +1
For a tetrahedron, suppose that all internal angles of faces and all dihedral angles are less than a fixed constant that is smaller than . Then, it is said to satisfy the ma…
Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We investigate the piecewise linear nonconforming Crouzeix-Raviar and the lowest order Raviart-Thomas finite-element methods for the Poisson problem on three-dimensional anisotropi…
General theory of interpolation error estimates on anisotropic meshes
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the d…