Work

Sobolev regularity of bivariate isogeometric finite element spaces in case of a geometry map with degenerate corner

Year: 2024

Type: article

Abstract: We investigate Sobolev regularity of bivariate functions obtained in Isogeometric Analysis when using geometry maps that are degenerate in the sense that the first partial derivatives vanish at isolated points. In particular, we show how the known $$C^1$$ C 1 -conditions for D-patches have to be tightened to guarantee square integrability of second partial derivatives, as required when computing finite element approximations of elliptic fourth order PDEs like the biharmonic equation.

Source: Advances in Computational Mathematics

DOI: 10.1007/s10444-024-10203-x

Author: Ulrich Reif

Institution: Technische Universität Darmstadt

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Technische Universität Darmstadt