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The concept of isogeometric analysis is proposed. Basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization. Analogues of finite element hand p-refinement schemes are… (More)

- Y Bazilevs, L Beirão Da Veiga, J A Cottrell, T J R Hughes, G Sangalli
- 2006

We begin the mathematical study of Isogeometric Analysis based on NURBS (non-uniform rational B-splines.) Isogeometric Analysis is a generalization of classical Finite Element Analysis (FEA) which possesses improved properties. For example, NURBS are capable of more precise geometric representation of complex objects and, in particular, can exactly… (More)

We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the ''stability norm'' are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that… (More)

- Y Bazilevs, V M Calo, J A Cottrell, J A Evans, T J R Hughes, S Lipton +2 others
- 2008

We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good… (More)

Weakly enforced Dirichlet boundary conditions are compared with strongly enforced conditions for boundary layer solutions of the advection-diffusion equation and incom-pressible Navier-Stokes equations. It is found that weakly enforced conditions are effective and superior to strongly enforced conditions. The numerical tests involve low-order finite… (More)

- T J R Hughes, A Reali, G Sangalli
- 2008

" In art economy is always beauty ". Abstract We initiate the study of efficient quadrature rules for NURBS-based isogeometric analysis. A rule of thumb emerges, the " half-point rule " , indicating that optimal rules involve a number of points roughly equal to half the number of degrees-of-freedom, or equivalently half the number of basis functions of the… (More)

We derive an explicit formula for the fine-scale Green's function arising in variational mul-tiscale analysis. The formula is expressed in terms of the classical Green's function and a projector which defines the decomposition of the solution into coarse and fine scales. The theory is presented in an abstract operator format and subsequently specialized for… (More)

We consider a family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements (both for the pressure and the flux variable). Instead of using a jump stabilization as it is usually done for DG methods (see e.g. [3], [13] and the references therein) we use the stabilization introduced in [18], [17]. We show that… (More)

A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two-and… (More)

- Y Bazilevs, V M Calo, Y Zhang, T J R Hughes
- 2006

A NURBS (non-uniform rational B-splines)-based isogeometric fluid-structure interaction formulation, coupling incompressible fluids with nonlinear elastic solids, and allowing for large structural displacements, is developed. This methodology, encompassing a very general class of applications, is applied to problems of arterial blood flow modeling and… (More)