Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Journal of Computational Physics
The p and hp versions of the finite element method for problems with boundary layers
Mathematics of Computation
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence
SIAM Journal on Numerical Analysis
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Analytic regularity for a singularly perturbed problem
SIAM Journal on Mathematical Analysis
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
An hp-Analysis of the Local Discontinuous Galerkin Method for Diffusion Problems
Journal of Scientific Computing
Thehp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
Mathematics of Computation
Journal of Scientific Computing
A review of the local discontinuous Galerkin (LDG) method applied to elliptic problems
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
Journal of Scientific Computing
Journal of Scientific Computing
Error analysis for optimal control problem governed by convection diffusion equations: DG method
Journal of Computational and Applied Mathematics
Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities
SIAM Journal on Numerical Analysis
A Fully-Discrete Local Discontinuous Galerkin Method for Convection-Dominated Sobolev Equation
Journal of Scientific Computing
A Superconvergent Local Discontinuous Galerkin Method for Elliptic Problems
Journal of Scientific Computing
Locking-Free Optimal Discontinuous Galerkin Methods for a Naghdi-Type Arch Model
Journal of Scientific Computing
Journal of Scientific Computing
Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
Numerical Algorithms
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We study the convergence properties of the hp-version of the local discontinuous Galerkin finite element method for convection-diffusion problems; we consider a model problem in a one-dimensional space domain. We allow arbitrary meshes and polynomial degree distributions and obtain upper bounds for the energy norm of the error which are explicit in the mesh-width h, in the polynomial degree p, and in the regularity of the exact solution. We identify a special numerical flux for which the estimates are optimal in both h and p. The theoretical results are confirmed in a series of numerical examples.