6 papers
Odd behaviour of even geometries: an explanation for superconvergent geometric consistency errors
Hanne Hardering, Simon Praetorius, Gentian Zavalani
Piecewise polynomial surface approximations used in surface finite element methods often seem to behave better than their standard approximation properties suggest if their polynom…
Cubature from rational approximation
Gentian Zavalani
We present a numerical construction of cubature rules for area integrals of analytic functions over planar domains with rectifiable Jordan boundary. The starting point is the Cauch…
The Bojanov--Naidenov inequality for quartics and second derivatives
Gentian Zavalani
We settle the case , of the Bojanov--Naidenov problem for algebraic polynomials. Let be a real polynomial of degree at most four with $\left\lVert{P}\right\rVert_{C[…
A High-Order Fast Direct Solver for Surface PDEs on Triangles
Gentian Zavalani
We develop a triangular formulation of the hierarchical Poincaré-Steklov (HPS) method for elliptic partial differential equations on surfaces, allowing high-order discretizations…
Fast high-order spectral solvers for PDEs on triangulated surfaces with applications to deforming surfaces
Gentian Zavalani
In this paper, we extend the classical quadrilateral based hierarchical Poincaré-Steklov (HPS) framework to triangulated geometries. Traditionally, the HPS method takes as input a…
High-order integration on regular triangulated manifolds reaches super-algebraic approximation rates through cubical re-parameterizations
Gentian Zavalani, Oliver Sander, Michael Hecht
We present a novel methodology for deriving high-order volume elements (HOVE) designed for the integration of scalar functions over regular embedded manifolds. For constructing HOV…