Error Estimate for Approximate Solutions Ofa Nonlinear Convection - Diffusion
نویسنده
چکیده
منابع مشابه
L1 error estimates for difference approximations of degenerate convection-diffusion equations
We analyze monotone finite difference schemes for strongly degenerate convection-diffusion equations in one spatial dimension. These nonlinear equations are well-posed within a class of (discontinuous) entropy solutions. We prove that the L1 error between the approximate and exact solutions is O(Δx1/3), where Δx is the spatial grid parameter. This result should be compared with the classical O(...
متن کاملError Estimate for Approximate Solutions of a Nonlinear Convection-diffusion Problem
This paper proves the estimate ‖uε − u‖L1(QT ) ≤ Cε , where, for all ε > 0, uε is the weak solution of (uε)t + div(q f(uε)) − ∆(φ(uε)+εuε) = 0 with initial and boundary conditions, u is the entropy weak solution of ut + div(qf(u)) − ∆(φ(u)) = 0 with the same initial and boundary conditions, and C > 0 does not depend on ε. The domain Ω is assumed to be regular and T is a given positive value.
متن کاملL1–framework for Continuous Dependence and Error Estimates for Quasilinear Anisotropic Degenerate Parabolic Equations
We develop a general L–framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach [9]. We apply our L–framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without t...
متن کاملL–framework for Continuous Dependence and Error Estimates for Quasilinear Anisotropic Degenerate Parabolic Equations
We develop a general L1–framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach [9]. We apply our L1–framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without...
متن کاملA nonlinear Discrete Duality Finite Volume Scheme for convection-diffusion equations
We introduce a nonlinear DDFV scheme for a convection-diffusion equation. The scheme conserves the mass, satisfies an energy-dissipation inequality and provides positive approximate solutions even on very general grids. Numerical experiments illustrate these properties.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002