Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Enhanced spectral viscosity approximations for conservation laws
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Spectral Differencing with a Twist
SIAM Journal on Scientific Computing
Journal of Scientific Computing
A Discontinuous Spectral Element Method for the Level Set Equation
Journal of Scientific Computing
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Computational Physics
Discontinuous Galerkin Methods Applied to Shock and Blast Problems
Journal of Scientific Computing
Adaptive unstructured volume remeshing - I: The method
Journal of Computational Physics
Journal of Computational Physics
The kink phenomenon in Fejér and Clenshaw–Curtis quadrature
Numerische Mathematik
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
A spectrally refined interface approach for simulating multiphase flows
Journal of Computational Physics
Hi-index | 31.45 |
It is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infinite-order convergence (also called spectral accuracy) when they are smooth (e.g., [C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods for Fluid Dynamics, Springer-Verlag, Heidelberg, 1988; J.P. Boyd, Chebyshev and Fourier Spectral Methods, second ed., Dover, New York, 2001; C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin Heidelberg, 2006]). If a discontinuity or a shock is present in the solution, this advantage is lost. There have been attempts to recover exponential convergence in such cases with rather limited success. The aim of this paper is to propose a discontinuous spectral element method coupled with a level set procedure, which tracks discontinuities in the solution of nonlinear hyperbolic conservation laws with spectral convergence in space. Spectral convergence is demonstrated in the case of the inviscid Burgers equation and the one-dimensional Euler equations.