Julia S. Mullen

Filter-based stabilization of spectral element methods.

Abstract We present a simple filtering procedure for stabilizing the spectral element method (SEM) for the unsteady advection–diffusion and Navier–Stokes equations. A number of example applications are presented, along with basic analysis for the advection–diffusion case.

A Fifth Order Flux Implicit WENO Method

The weighted essentially non-oscillatory (WENO) method is an excellent spatial discretization for hyperbolic partial differential equations with discontinuous solutions. However, the time-step restriction associated with explicit methods may pose severe limitations on their use in applications requiring large scale computations. An efficient implicit WENO method is necessary. In this paper, we propose a prototype flux-implicit WENO (iWENO) method. Numerical tests on classical scalar equations show that this is a viable and stable method, which requires appropriate time-stepping methods. Future study will include the examination of such methods as well as extension of iWENO to systems and higher dimensional problems.

An implicit WENO scheme for steady-state computation of scalar hyperbolic equations

Publisher Summary This chapter addresses an implicit weighted essentially nonoscillatory (WENO) scheme for steady-state computation of scalar hyperbolic equations. WENO schemes are high-order finite-difference methods with an adaptive-stencil approach. These schemes have proved useful in a variety of physical applications. They capture sharp gradients without smearing, and feature high order of accuracy along with nonlinear stability. The high order of accuracy, robustness, and smooth numerical fluxes of the WENO schemes make them ideal for use with Jacobian-based iterative solvers, to directly simulate the steady-state solution of conservation laws. The chapter focuses on a Newton-based implicit WENO solver for scalar conservation laws. A unique interpolation technique is developed, which produces a more efficient iteration. Numerical results are also presented.

Student-perceived effectiveness of online content delivery modes

This Work In Progress focuses on student perceptions of the effectiveness of three content delivery modes; a) traditional, residential in-class b) class capture for asynchronous online delivery, and c) modularized targeted content videos for online and blended or flipped classroom mode. Despite the growth of MOOCs and the concomitant shift from long lecture videos to learning modules, many online courses still rely on a class capture method. A recent study on video use by students in online courses recommends the use of short videos, six to nine minutes in length, based on student viewing habits. [1] The student behavior was inferred from click-stream data captured within the LMS but there was no direct interaction with students to gauge impressions of the content delivery or impact on learning. To improve both the residential and online experience requires a deeper understanding of those features which promote learning in each approach. Some of this understanding can be gleaned from traditional academic course evaluations, but student perceptions yield an additional level of understanding. For this study we analyzed data from multiple offerings of a 7-week graduate level numerical analysis course; Application of Finite Element Analysis. Over three years this course was offered residentially and online using multiple delivery modes. We categorize the delivery modes as Traditional, Class-Capture, and Modularized/Blended. Each student studied the material using one delivery mode and was then asked to review the material using another delivery mode. The students were asked to evaluate the perceived learning attained based on their original content delivery mode and the alternate mode. The feedback from this analysis, combined with traditional course evaluations will be used to develop a more comprehensive and objective survey to be used in the next round of courses.