Scalable adaptive mantle convection simulation on petascale supercomputers
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Polymorphic nodal elements and their application in discontinuous Galerkin methods
Journal of Computational Physics
The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem
Journal of Scientific Computing
A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics
Journal of Scientific Computing
Nodal discontinuous Galerkin methods on graphics processors
Journal of Computational Physics
Stable Boundary Treatment for the Wave Equation on Second-Order Form
Journal of Scientific Computing
Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Local time stepping and discontinuous Galerkin methods for symmetric first order hyperbolic systems
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Explicit local time-stepping methods for Maxwell's equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy
Journal of Scientific Computing
Journal of Computational Physics
A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows
Journal of Computational Physics
Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty
Applied Numerical Mathematics
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Journal of Computational Physics
Applied Numerical Mathematics
A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods
Journal of Scientific Computing
A Hybrid Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
SIAM Journal on Scientific Computing
CFL Conditions for Runge-Kutta discontinuous Galerkin methods on triangular grids
Journal of Computational Physics
Numerical analysis of a PML model for time-dependent Maxwell's equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Two-Grid Discontinuous Galerkin Method for Quasi-Linear Elliptic Problems
Journal of Scientific Computing
Efficient low-storage Runge-Kutta schemes with optimized stability regions
Journal of Computational Physics
Scalable Direct Vlasov Solver with Discontinuous Galerkin Method on Unstructured Mesh
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
On the Non-linear Stability of Flux Reconstruction Schemes
Journal of Scientific Computing
Journal of Scientific Computing
A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements
Journal of Scientific Computing
A Fully-Discrete Local Discontinuous Galerkin Method for Convection-Dominated Sobolev Equation
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
I/O threads to reduce checkpoint blocking for an electromagnetics solver on Blue Gene/P and Cray XK6
Proceedings of the 2nd International Workshop on Runtime and Operating Systems for Supercomputers
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Developing Finite Element Methods for Maxwell's Equations in a Cole-Cole Dispersive Medium
SIAM Journal on Scientific Computing
Journal of Computational Physics
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Journal of Computational Physics
Method of Moving Frames to Solve Conservation Laws on Curved Surfaces
Journal of Scientific Computing
An analysis of the spectrum of the discontinuous Galerkin method
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Numerical Study of the Plasma-Lorentz Model in Metamaterials
Journal of Scientific Computing
A space-time smooth artificial viscosity method for nonlinear conservation laws
Journal of Computational Physics
The generation of arbitrary order curved meshes for 3D finite element analysis
Computational Mechanics
Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations
Journal of Computational Physics
GPU accelerated discontinuous Galerkin methods for Euler equations and its adjoint
Proceedings of the High Performance Computing Symposium
Energy stable flux reconstruction schemes for advection-diffusion problems on triangles
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Robust untangling of curvilinear meshes
Journal of Computational Physics
Journal of Computational Physics
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
Causal-Path Local Time-Stepping in the discontinuous Galerkin method for Maxwell's equations
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Scientific Computing
Stable multi-domain spectral penalty methods for fractional partial differential equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The Double Absorbing Boundary method
Journal of Computational Physics
Dispersive behaviour of high order finite element schemes for the one-way wave equation
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 0.18 |
The text offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. All key theoretical results are either derived or discussed, including an overview of relevant results from approximation theory, convergence theory for numerical PDEs, orthogonal polynomials etc. Through embedded Matlab codes, the algorithms are discussed and implemented for a number of classic systems of PDEs, e.g., Maxwells equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations. These developments are done in detail inone and two dimensions on general unstructured grids with high-order elements and all essential routines for 3D extensions are also included and discussed briefly. The three appendices contain an overview of orthogonal polynomials and associated library routines used throughout, a brief introduction to grid generation, and an overview of the associated software (where to get it, list of variables etc). A variety of exercises are included at the end of most chapters.