On the divergence constraint in mixed finite element methods for incompressible flows

V John, A Linke, C Merdon, M Neilan, LG Rebholz - SIAM review, 2017‏ - SIAM
The divergence constraint of the incompressible Navier--Stokes equations is revisited in the
mixed finite element framework. While many stable and convergent mixed elements have …

An insight on NURBS based isogeometric analysis, its current status and involvement in mechanical applications

V Gupta, A Jameel, SK Verma, S Anand… - Archives of Computational …, 2023‏ - Springer
The current communication is a state-of-the-art review of the recently developed
Isogeometric analysis and its various applications such as structural, thermal, fluid–structure …

Divergence free virtual elements for the Stokes problem on polygonal meshes

LB da Veiga, C Lovadina, G Vacca - … : Mathematical Modelling and …, 2017‏ - esaim-m2an.org
In the present paper we develop a new family of Virtual Elements for the Stokes problem on
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …

[HTML][HTML] A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0

R Vázquez - Computers & Mathematics with Applications, 2016‏ - Elsevier
Abstract GeoPDEs (http://rafavzqz. github. io/geopdes) is an Octave/Matlab package for the
solution of partial differential equations with isogeometric analysis, first released in 2010. In …

GeoPDEs: a research tool for isogeometric analysis of PDEs

C De Falco, A Reali, R Vázquez - Advances in Engineering Software, 2011‏ - Elsevier
GeoPDEs (http://geopdes. sourceforge. net) is a suite of free software tools for applications
on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the …

Mathematical analysis of variational isogeometric methods

LB Da Veiga, A Buffa, G Sangalli, R Vázquez - Acta Numerica, 2014‏ - cambridge.org
This review paper collects several results that form part of the theoretical foundation of
isogeometric methods. We analyse variational techniques for the numerical resolution of …

A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis

F Auricchio, F Calabro, TJR Hughes, A Reali… - Computer Methods in …, 2012‏ - Elsevier
We develop new quadrature rules for isogeometric analysis based on the solution of a local
nonlinear problem. A simple and robust algorithm is developed to determine the rules which …

Isogeometric discrete differential forms in three dimensions

A Buffa, J Rivas, G Sangalli, R Vázquez - SIAM Journal on Numerical Analysis, 2011‏ - SIAM
The concept of isogeometric analysis (IGA) was first applied to the approximation of Maxwell
equations in [A. Buffa, G. Sangalli, and R. Vázquez, Comput. Methods Appl. Mech. Engrg …

Conforming and divergence-free Stokes elements on general triangular meshes

J Guzmán, M Neilan - Mathematics of Computation, 2014‏ - ams.org
We present a family of conforming finite elements for the Stokes problem on general
triangular meshes in two dimensions. The lowest order case consists of enriched piecewise …

Seamless integration of design and Kirchhoff–Love shell analysis using analysis-suitable unstructured T-splines

H Casquero, X Wei, D Toshniwal, A Li… - Computer Methods in …, 2020‏ - Elsevier
Abstract Analysis-suitable T-splines (ASTS) including both extraordinary points and T-
junctions are used to solve Kirchhoff–Love shell problems. Extraordinary points are required …