Error Estimate for Approximate Solutions of a Nonlinear Convection-diffusion Problem

Error Estimate for Approximate Solutions Ofa Nonlinear Convection - Diffusion

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(...

Higher-Order Linear-Time Unconditionally Stable Alternating Direction Implicit Methods for Nonlinear Convection-Diffusion Partial Differential Equation Systems

We introduce a class of alternating direction implicit (ADI) methods, based on approximate factorizations of backward differentiation formulas (BDFs) of order p 2, for the numerical solution of two-dimensional, time-dependent, nonlinear, convection-diffusion partial differential equation (PDE) systems in Cartesian domains. The proposed algorithms, which do not require the solution of nonlinear ...

Higher-Order Linear-Time Unconditionally Stable ADI Methods for Nonlinear Convection-Diffusion PDE Systems

We introduce a class of alternating direction implicit (ADI) methods, based on approximate factorizations of backward differentiation formulas (BDF) of order p ≥ 2, for the numerical solution of two-dimensional, timedependent, nonlinear, convection-diffusion PDE systems in Cartesian domains. The proposed algorithms, which do not require solution of nonlinear systems, additionally produce soluti...

An Operator Splitting Method for Nonlinear Convection-diffusion Equations

We present a semi discrete method for constructing approximate solutions to the initial value problem for the m dimensional convection di usion equation ut r f u u The method is based on the use of operator splitting to isolate the convection part and the di usion part of the equation In the casem dimensional splitting is used to reduce the m dimensional convection problem to a series of one di...