Browsing by Author "Bonito, Andrea"
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Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H. (SIAM Journal on Numerical Analysis, 2013) 
An Energy Formulation of Surface Tension or Willmore Force For TwoPhase Flow
Patty, Spencer (20170712)The motion of a biological cell in liquid is a rich subject for modeling. In the early 1970’s, it was realized by Canham that biological vesicles with lipid bilayer membranes reach a steady state shape that minimizes ... 
Continuous Finite Element Approximation of Hyperbolic Systems
Yang, Yong (20160613)The main purpose of this work is to study continuous finite element methods for hyperbolic problems. In scalar case, it is shown that using consistent mass matrix is not compatible with the maximum principle. Moreover, we ... 
Convergence and Optimality of HigherOrder Adaptive Finite Element Methods for Eigenvalue Clusters
Bonito, Andrea; Demlow, Alan (SIAM Journal on Numerical Analysis, 2016) 
Dynamic Adaptive Multimesh Refinement for Coupled Physics Equations Applicable to Nuclear Engineering
Dugan, Kevin (20130621)The processes studied by nuclear engineers generally include coupled physics phenomena (ThermalHydraulics, Neutronics, Material Mechanics, etc.) and modeling such multiphysics processes numerically can be computationally ... 
Finite Element Approximation of Eigenvalues and Eigenfunctions of the LaplaceBeltrami Operator
Owen, Justin Ian (20190903)The surface finite element method is an important tool for discretizing and solving elliptic partial differential equations on surfaces. Recently the surface finite element method has been used for computing approximate ... 
An Interior Penalty Method with C 0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity
Bonito, Andrea; Guermond, JeanLuc; Luddens, Francky (Mathematical Modelling and Numerical Analysis / Modélisation mathématique et analyse numérique, 2016) 
Modelling Flow through Porous Media under Large Pressure Gradients
Srinivasan, Shriram (20131101)The most interesting and technologically important problems in the study of flow through porous media involve very high pressures and pressure gradients in the flow do main such as enhanced oil recovery and carbon dioxide ... 
Numerical Approximation of Partial Differential Equations Involving Fractional Differential Operators
Lei, Wenyu (20180522)The negative powers of an elliptic operator can be approximated via its DunfordTaylor integral representation, i.e. we approximate the DunfordTaylor integral with an exponential convergent sinc quadrature scheme and ... 
Numerical Approximation of Time Dependent Fractional Diffusion With Drift: Numerical Analysis and Applications to Surface QuasiGeostrophic Dynamics and Electroconvection
Wei, Peng (20190624)In this work, we approximate a timedependent problem with drift involving fractional powers of elliptic operators. The numerical scheme is based on an integral representation of the stationary problem at each time step. ... 
Numerical Approximation of Time Dependent Fractional Diffusion With Drift: Numerical Analysis and Applications to Surface QuasiGeostrophic Dynamics and Electroconvection
Wei, Peng (20190624)In this work, we approximate a timedependent problem with drift involving fractional powers of elliptic operators. The numerical scheme is based on an integral representation of the stationary problem at each time step. ... 
Numerical Simulations of Bouncing Jets
Lee, Sanghyun (20140718)The Kaye effect is a fascinating phenomenon of a leaping shampoo stream which was first described by Alan Kaye in 1963 as a property of nonNewtonian fluid. It manifest itself when a thin stream of nonNewtonian fluid is ... 
On Strong Ellipticity and Monotonicity for Implicit and StrainLimiting Theories of Elasticity
Mai, Na (20150501)There has been increasing interest in the archival literature devoted to the study of implicit constitutive theories for nondissipative materials generalizing the classical Green and Cauchy notions of elasticity, and for ... 
On the Electromagnetic Fields in Planar Layered Media Comprising Anisotropic Conductive Sheets at the Interfaces
Mustafa, Mazin Mohamed Musa (20190711)The recent revolution in twodimensional materials, such as graphene monolayers, has attracted many researchers to investigate their properties and potential applications in different fields. The 2D materials are usually ... 
On the Electromagnetic Fields in Planar Layered Media Comprising Anisotropic Conductive Sheets at the Interfaces
Mustafa, Mazin Mohamed Musa (20190711)The recent revolution in twodimensional materials, such as graphene monolayers, has attracted many researchers to investigate their properties and potential applications in different fields. The 2D materials are usually ... 
Parallel Multiphase NavierStokes Solver
Alrashed, Fahad Saleh (20150504)We study and implement methods to solve the variable density NavierStokes equations. More specifically, we study the transport equation with the level set method and the momentum equation using two methods: the projection ... 
QuasiOptimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
Bonito, Andrea; Nochetto, Ricardo H. (SIAM Journal on Numerical Analysis, 2010) 
Regularizing Inverse Problems
Wang, Fang (20140626)An inverse problem reconstructs the unknown internal parameters of a subject based on collected data derived synthetically or from real measurements. Inverse problems often lack the wellposedness defined by J. Hadamard; ... 
Residual and GoalOriented h and hpadaptive Finite Element; Application for Elliptic and Saddle Point Problems
Ghesmati, Arezou (20180118)We propose and implement an automatic hpadaptive refinement algorithm for the Stokes model problem. In this work, the strategy is based on the earlier work done by Dörfler at al. in 2007 for the Poisson problem. Similar ... 
Selective StrongField Enhancement and Attenuation of Excitation and Ionization with Short Laser Pulses
Hart, Nathan Andrew (20150512)The coherent control of atomic energy level population is important for several areas physics and engineering including fluorescent spectroscopy, resonantly enhanced multiphoton ionization, harmonic generation, remote ...