Wave Resolution Properties and Weighted Essentially Non-Oscillatory Limiter for Discontinuous Galerkin Methods Zhong, Xinghui creator 2012 xvii, 122 p. born digital Thesis (Ph.D. -- Brown University (2012) Shu, Chi-Wang Director Guzman, Johnny Reader Hesthaven, Jan Reader Brown University. Applied Mathematics sponsor theses discontinuous Galerkin method error analysis superconvergence,fully discretized,points per wavelength,WENO limiter Error analysis (Mathematics) RPB 20121023 engEnglishThis dissertation presents wave resolution properties and weighted essentially non-oscillatory limiter for discontinuous Galerkin methods solving hyperbolic conservation laws. <br/> <br/> In this dissertation, using Fourier analysis, we provide a quantitative error analysis for the semi-discrete DG method applied to time dependent linear convection equations with periodic boundary conditions. We apply the same technique to show that the error is of order $k+2$ superconvergent at Radau points on each element and of order $2k+1$ superconvergent at the downwind point of each element, when using piecewise polynomials of degree $k$. An analysis of the fully discretized approximation is also provided. We compute the number of points per wavelength required to obtain a fixed error <br/> for several fully discrete schemes. <br/> <br/> We also investigate a simple limiter using<br/> weighted essentially non-oscillatory (WENO) methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving conservation laws, with the goal of obtaining a robust<br/> and high order limiting procedure to simultaneously achieve uniform high order accuracy and sharp, non-oscillatory shock transitions. The idea of this limiter is to reconstruct the entire polynomial, instead of reconstructing point values or moments in <br/> the classical WENO reconstructions. That is, the reconstruction polynomial on the target cell is a convex combination of polynomials on this cell and its neighboring cells and the nonlinear weights of the convex combination follow the <br/> classical WENO procedure. The main advantage of this limiter is its simplicity in implementation, especially for multi-dimensional meshes.<br/> <br/>10.7301/Z0ZW1J6DIn CopyrightCollection is open for research.dissertations