In this paper we analyze local properties of the Continuous Interior Penalty (CIP) Method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows that locally, the CIP method is comparable to the Streamline Diffusion (SD) or t...

A defect-correction mixed finite element method for solving the time-dependent JohnsonSegalman viscoelastic equations in two dimensions is given. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step on the same grid. A streamline upwind PetrovGalerkin SUPG appro...

      Many large oil and gas fields in the most productive world regions happen to be fractured. The exploration and development of these reservoirs is a true challenge for many operators. These difficulties are due to uncertainties in geological fracture properties such as aperture, length, connectivity and intensity distribution. To successfully address these challenges, it is paramount to im...

Streamline visualization can be formulated as the problem of streamline placement or streamline selection. In this paper, we present an importance-driven approach to view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. Given a large number of randomly or uniformly seeded and traced streamlines and sample viewpoints, our approach evaluat...

The stability and accuracy of a streamline diffusion finite element method (SDFEM) on arbitrary grids applied to a linear 1-d singularly perturbed problem are studied in this paper. With a special choice of the stabilization quadratic bubble function, the SDFEM is shown to have an optimal second order in the sense that ‖u − uh‖∞ ≤ C infvh∈V h ‖u − vh‖∞, where uh is the SDFEM approximation of th...

The analysis and visualization of flows is a central problem in visualization. Topology based methods have gained increasing interest in recent years. This article describes a method for the detection of closed streamlines in 3D flows. It is based on a special treatment of cases where a streamline reenters a cell to prevent infinite cycling during streamline calculation. The algorithm checks fo...

We introduce a fibre tract segmentation algorithm based on the geometric coherence of fibre orientations as indicated by a streamline flow model. The inference of local flow approximations motivates a pairwise consistency measure between fibre ODF maxima. We use this measure in a recursive algorithm to cluster consistent ODF maxima, leading to the segmentation of white matter pathways. The meth...

The PHLIpS (Producing Hands-on Learning to InsPire Students) Method provides a systematic approach for professors desiring to develop active learning activities for their classrooms. Many professors appreciate the benefits of active learning and wish to include more activities in their classroom. Unfortunately, activities for a given topic or course are commonly not available as an off-the-self...

We obtain curvature estimates for long-time solutions of the continuity method on compact Kähler manifolds with semi-ample canonical line bundles. In this setting, initiated in [G. La Nave and G. Tian, A to construct metrics, Math. Ann. 365(3) (2016) 911–921; Y. A. Rubinstein, Some discretizations geometric evolution equations Ricci iteration space Adv. 218(5) (2008) 1526–1565], we adapt argume...

A fractional step θ-method for the approximation of time dependent viscoelastic fluid flow equations, is described and analyzed in this article. The θ-method implementation allows the velocity and pressure updates to be resolved separately from the stress, reducing the number of unknowns resolved at each step of the method. A streamline upwinded Petrov-Galerkin (SUPG)-method is used to stabiliz...