We propose a Scott-Zhang type interpolation operator for the approximation of non-smooth functions in H1 by means of continuous piecewise polynomials of low order. The novelty of the proposed interpolation operator is that it is defined for a general non-affine family of quadrilateral and hexahedral meshes with possibly hanging nodes. The derived interpolator exhibits optimal approximation prop...

This fact motivated the rise of alternative simulation approaches (Lattice Boltzmann, Finite Differences, Finite Element Embedded approaches), which approximate the shape of the object of interest by the use of local refinement techniques or simply by employing finer discretizations. Within the area of the Finite Element Method (FEM), the challenge its often addressed by the use of tetrahedral ...

In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with impurities general geometry. The proposed does not require background mesh fit interfaces impurities, and thus avoids expensive cost generating body-fitted meshes simplifies inclusion interface conditions in formulation. quasi-periodic boundary are handled by Floquet-Bloch transform, w...

We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, lumenal surfaces are e...

The development of robust high-order finite element methods requires the construction of valid high-order meshes for complex geometries without user intervention. This paper presents a novel approach for automatically generating a high-order mesh with two main features: first, the boundary of the mesh is globally smooth; second, the mesh boundary satisfies a required fidelity tolerance. Invalid...

The time dependent transport equation is solved with stabilized continuous, piecewise linear finite elements and the Crank-Nicolson scheme [1]. Finite elements with large aspect ratio are advocated in order to account for boundary layers. The error due to space discretization has already been studied in [2]. Here, the error due to the use of the Crank-Nicolson scheme is taken into account. Anis...

This paper presents a numerically stable method for rigid body simulation of unstructured meshes undergoing forceful contact, such as in robot locomotion and manipulation. The key contribution is a new contact generation method that treats the geometry as having a thin virtual boundary layer around the underlying meshes. Unlike existing methods, it produces contact estimates that are stable wit...

We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, lumenal surfaces are e...

Abstract. “Discrete Duality Finite Volume” schemes (DDFV for short) on general meshes are studied here for Stokes problems with variable viscosity with Dirichlet boundary conditions. The aim of this work is to analyze the well-posedness of the scheme and its convergence properties. The DDFV method requires a staggered scheme, the discrete unknowns, the components of the velocity and the pressur...