4 papers
Anisotropic Lagrange interpolation on exact spherical triangles
Hiroki Ishizaka
We study linear Lagrange interpolation on exact geodesic spherical triangles obtained by radial projection of chordal triangles. Factorising the element map into an affine map and…
Exact-curved Lagrange finite elements for the Poisson problem in two dimensions
Hiroki Ishizaka
Conforming mapped Lagrange finite elements of any fixed degree are analysed for the Poisson problem on exact curved triangulations in two dimensions. The element map is factorised…
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…
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…