Accession Number : ADA632321


Title :   A Study into Discontinuous Galerkin Methods for the Second Order Wave Equation


Descriptive Note : Master's thesis


Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA


Personal Author(s) : Davis, Benjamin J


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a632321.pdf


Report Date : Jun 2015


Pagination or Media Count : 151


Abstract : There are numerous numerical methods for solving different types of partial differential equations (PDEs) that describe the physical dynamics of the world. For instance, PDEs are used to understand fluid flow for aerodynamics, wave dynamics for seismic exploration, and orbital mechanics. The goal of these numerical methods is to approximate the solution to a continuous PDE with an accurate discrete representation. The focus of this thesis is to explore a new Discontinuous Galerkin (DG) method for approximating the second order wave equation in complex geometries with curved elements. We begin by briefly highlighting some of the numerical methods used to solve PDEs and discuss the necessary concepts to understand DG methods. These concepts are used to develop a one- and two-dimensional DG method with an upwind flux, boundary conditions, and curved elements. We demonstrate convergence numerically and prove discrete stability of the method through an energy analysis.


Descriptors :   *GALERKIN METHOD , *PARTIAL DIFFERENTIAL EQUATIONS , *WAVE EQUATIONS , ACOUSTIC WAVES , CONVERGENCE , DISCRETE DISTRIBUTION , FINITE DIFFERENCE TIME DOMAIN , FINITE ELEMENT ANALYSIS , FLUID FLOW , FLUX(RATE) , NUMERICAL METHODS AND PROCEDURES , PHYSICAL PROPERTIES , SEISMOLOGY , STABILITY , THESES


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE