On the Coupling of Local Discontinuous Galerkin and Conforming Finite Element Methods
Journal of Scientific Computing
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
Journal of Scientific Computing
Block Preconditioners for LDG Discretizations of Linear Incompressible Flow Problems
Journal of Scientific Computing
Discontinuous Galerkin Method for Linear Free-Surface Gravity Waves
Journal of Scientific Computing
An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method
Journal of Scientific Computing
A mixed local discontinuous Galerkin method for a class of nonlinear problems in fluid mechanics
Journal of Computational Physics
Journal of Scientific Computing
Journal of Scientific Computing
An a posteriori error estimate for the local discontinuous Galerkin method
Journal of Scientific Computing
Block preconditioners for LDG discretizations of linear incompressible flow problems
Journal of Scientific Computing
Discontinuous Galerkin method for linear free-surface gravity waves
Journal of Scientific Computing
Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations
Journal of Computational Physics
A class of difference schemes with flexible local approximation
Journal of Computational Physics
A unified analysis of the local discontinuous Galerkin method for a class of nonlinear problems
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
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)
A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations
Journal of Scientific Computing
Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Higher-order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements
Journal of Scientific Computing
Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems
Calcolo: a quarterly on numerical analysis and theory of computation
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
Journal of Scientific Computing
Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions
Journal of Scientific Computing
A Hybrid Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Adaptive discontinuous Galerkin B-splines on parametric geometries
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
The new numerical method for solving the system of two-dimensional Burgers' equations
Computers & Mathematics with Applications
Analysis of the DPG Method for the Poisson Equation
SIAM Journal on Numerical Analysis
On the Negative-Order Norm Accuracy of a Local-Structure-Preserving LDG Method
Journal of Scientific Computing
To CG or to HDG: A Comparative Study
Journal of Scientific Computing
A Superconvergent Local Discontinuous Galerkin Method for Elliptic Problems
Journal of Scientific Computing
SIAM Journal on Scientific Computing
A weak Galerkin finite element method for second-order elliptic problems
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
A Coupling of Local Discontinuous Galerkin and Natural Boundary Element Method for Exterior Problems
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Scientific Computing
The DPG method for the Stokes problem
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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In this paper, we present the first a priori error analysis for the local discontinuous Galerkin (LDG) method for a model elliptic problem. For arbitrary meshes with hanging nodes and elements of various shapes, we show that, for stabilization parameters of order one, the L2-norm of the gradient and the L2-norm of the potential are of order k and k+1/2, respectively, when polynomials of total degree at least k are used; if stabilization parameters of order h-1 are taken, the order of convergence of the potential increases to k+1. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains.