Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations
نویسندگان
چکیده
منابع مشابه
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations
Abstract. In this paper, we present the optimal L2-error estimate ofO(hk+1) for polynomial elements of degree k of the semidiscrete direct discontinuous Galerkin method for convection-diffusion equations. The main technical difficulty lies in the control of the inter-element jump terms which arise because of the convection and the discontinuous nature of numerical solutions. The main idea is to...
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 کاملDiscontinuous Galerkin Method for Fractional Convection-Diffusion Equations
We propose a discontinuous Galerkin method for fractional convection-diffusion equations with a superdiffusion operator of order α(1 < α < 2) defined through the fractional Laplacian. The fractional operator of order α is expressed as a composite of first order derivatives and a fractional integral of order 2 − α. The fractional convection-diffusion problem is expressed as a system of low order...
متن کاملA posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations
A posteriori error estimates are derived for unsteady convection-diffusion equations discretized with the non-symmetric interior penalty and the local discontinuous Galerkin methods. First, an error representation formula in a user specified output functional is derived using duality techniques. Then, an Lt (L 2 x) a posteriori estimate consisting of elementwise residual-based error indicators ...
متن کاملOptimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems
We study the convergence properties of the hp-version of the local discontinuous Galerkin finite element method for convection-diffusion problems; we consider a model problem in a one-dimensional space domain. We allow arbitrary meshes and polynomial degree distributions and obtain upper bounds for the energy norm of the error which are explicit in the mesh-width h, in the polynomial degree p, ...
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: Mathematics of Computation
سال: 2015
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2015-02923-8