Ana posteriorierror bound for discontinuous Galerkin approximations of convection–diffusion problems
نویسندگان
چکیده
منابع مشابه
Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems
In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, a...
متن کاملAdaptive discontinuous Galerkin approximations to fourth order parabolic problems
Abstract. An adaptive algorithm, based on residual type a posteriori indicators of errors measured in L∞(L2) and L2(L2) norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local s...
متن کاملEfficient computable error bounds for discontinuous Galerkin approximations of elliptic problems
We present guaranteed and computable both sided error bounds for the discontinuous Galerkin (DG) approximations of elliptic problems. These estimates are derived in the full DG-norm on purely functional grounds by the analysis of the respective differential problem, and thus, are applicable to any qualified DG approximation. Based on the triangle inequality, the underlying approach has the foll...
متن کاملMultilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients
In this article we develop and analyze two-level and multi-level methods for the family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic problems with rough coefficients (exhibiting large jumps across interfaces in the domain). These methods are based on a decomposition of the DG finite element space that inherently hinges on the diffusion coefficien...
متن کاملA-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems
Using the weighted residual formulation we derive a-posteriori estimates for Discontinuous Galerkin approximations of second order elliptic problems in mixed form. We show that our approach allows to include in a unified way all the methods presented so far in the literature.
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: IMA Journal of Numerical Analysis
سال: 2017
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drx065