An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations
نویسندگان
چکیده
An oscillation free local discontinuous Galerkin (OFLDG) method is proposed for solving nonlinear degenerate parabolic equations. The damping terms are added to the original LDG scheme control spurious oscillations when solutions have a large gradient. L2-stability and optimal priori error estimates semi-discrete in one- multi-dimensions established. numerical experiments demonstrate that maintains high order accuracy controls well.
منابع مشابه
A Discontinuous Galerkin Method Applied to Nonlinear Parabolic Equations
Semi-discrete and a family of discrete time locally conservative Dis-continuous Galerkin procedures are formulated for approximations to nonlinear parabolic equations. For the continuous time approximations a priori L 1 (L 2) and L 2 (H 1) estimates are derived and similarly, l 1 (L 2) and l 2 (H 1) for the discrete time schemes. Spatial rates in H 1 and time truncation errors in L 2 are optimal.
متن کاملAn hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an...
متن کاملThe discontinuous Galerkin method for fractional degenerate convection-diffusion equations
We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through n...
متن کاملLocal Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations
This paper is concerned with developing accurate and efficient nonstandard discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary goal of the paper to develop a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity...
متن کاملLocal discontinuous Galerkin methods for nonlinear dispersive equations
We develop local discontinuous Galerkin (DG) methods for solving nonlinear dispersive partial differential equations that have compactly supported traveling waves solutions, the so-called ‘‘compactons’’. The schemes we present extend the previous works of Yan and Shu on approximating solutions for linear dispersive equations and for certain KdV-type equations. We present two classes of DG metho...
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: Numerical Methods for Partial Differential Equations
سال: 2023
ISSN: ['1098-2426', '0749-159X']
DOI: https://doi.org/10.1002/num.23003