3 papers
math.NA2026
Exact-curved Lagrange finite elements for the Poisson problem in two dimensions
Hiroki Ishizaka
We develop an exact-curved Lagrange finite element framework for the Poisson problem on two-dimensional curved domains. The element map is factorised as , w…
math.NA2026
On discrete Sobolev inequalities for nonconforming finite elements under a semi-regular mesh condition
Hiroki Ishizaka
We derive a discrete Sobolev inequality tailored for the Crouzeix--Raviart and discontinuous Crouzeix--Raviart finite element spaces on anisotropic meshes in both two an…
math.NA2025
Interpolation error analysis using a new geometric parameter
Hiroki Ishizaka
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the fi…