Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
On a cell entropy inequality for discontinuous Galerkin methods
Mathematics of Computation
Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
Journal of Scientific Computing
Discontinuous Galerkin methods with plane waves for time-harmonic problems
Journal of Computational Physics
Journal of Scientific Computing
A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations
Journal of Scientific Computing
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
Journal of Computational Physics
On the Negative-Order Norm Accuracy of a Local-Structure-Preserving LDG Method
Journal of Scientific Computing
Journal of Scientific Computing
Hi-index | 31.46 |
In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific types of PDEs and initial and boundary conditions. It is shown that L2 stability and error estimates can be obtained when the approximation space is suitably selected. It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy.