Mixed Isogeometric Analysis of the Brinkman Equation

Abstract

This study focuses on numerical solution to the Brinkman equation with mixed Dirichlet–Neumann boundary conditions utilizing isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS) within the Galerkin method framework. The authors suggest using different choices of compatible NURBS spaces, which may be considered a generalization of traditional finite element spaces for velocity and pressure approximation. In order to investigate the numerical properties of the suggested elements, two numerical experiments based on a square and a quarter of an annulus are discussed. The preliminary results for the Stokes problem are presented in References.