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Full-Text Articles in Numerical Analysis and Computation
Advection-Reaction-Diffusion Model Of Drug Concentration In A Lymph Node, Ting Yan
Advection-Reaction-Diffusion Model Of Drug Concentration In A Lymph Node, Ting Yan
Mathematics Theses and Dissertations
It is recognized that there exist reservoirs of HIV located outside the bloodstream, and that these reservoirs hinder the efficacy of antiretroviral medication regimens in combating the virus. The prevailing theories regarding these reservoirs point to the lymphatic system. In this work, we discuss a novel computational model of viral dynamics in the lymph node, to allow numerical studies of viral “reservoirs” causing reinfection. Our model consists of a system of advection-reaction-diffusion partial differential equations (PDEs), where the diffusion coefficients vary between species (virus, drugs, lymphocytes) and include discontinuous jumps to capture differing properties of internal lymph node structures. We …
A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang
A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang
Mathematics Theses and Dissertations
Discontinuous Galerkin methods are widely used in many practical fields. In this thesis, we focus on a new class of discontinuous Galerkin methods for second-order wave equations. This thesis is constructed by three main parts. In the first part, we study the convergence properties of the energy-based discontinuous Galerkin proposed in [3] for wave equations. We improve the existing suboptimal error estimates to an optimal convergence rate in the energy norm. In the second part, we generalize the energy-based discontinuous Galerkin method proposed in [3] to the advective wave equation and semilinear wave equation in second-order form. Energy-conserving or energy-dissipating …