Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection–diffusion problems: Insights into spectral vanishing viscosity
نویسندگان
چکیده
منابع مشابه
Spectral Viscosity Approximations to Hamilton-Jacobi Solutions
The spectral viscosity approximate solution of convex Hamilton–Jacobi equations with periodic boundary conditions is studied. It is proved in this paper that the approximation and its gradient remain uniformly bounded, formally spectral accurate, and converge to the unique viscosity solution. The L1-convergence rate of the order 1− ε∀ε > 0 is obtained.
متن کاملSpectral Vanishing Viscosity Method for Nonlinear
We propose a new spectral viscosity (SV) scheme for the accurate solution of nonlinear conservation laws. It is proved that the SV solution converges to the unique entropy solution under appropriate reasonable conditions. The proposed SV scheme is implemented directly on high modes of the computed solution. This should be compared with the original nonperiodic SV scheme introduced by Maday, Oul...
متن کاملFractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods
We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the co...
متن کاملOn the Convergence Rate of Vanishing Viscosity Approximations
Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound ‖u(t, · )− uε(t, · )‖L1 = O(1)(1 + t) · √ ε |ln ε| on the distance between an exact BV solution u and a viscous approximation uε , letting the viscosity coefficient ε → 0. In the proof, starting from u we construct an approximation of the viscous solution uε by taking a mollification u ∗ φ√...
متن کاملSpectral Viscosity Approximations to Multidimensional Scalar Conservation Laws
We study the spectral viscosity (SV) method in the context of multidimensional scalar conservation laws with periodic boundary conditions. We show that the spectral viscosity, which is sufficiently small to retain the formal spectral accuracy of the underlying Fourier approximation, is large enough to enforce the correct amount of entropy dissipation (which is otherwise missing in the standard ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2016
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2015.12.009