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- Title
Functional A Posteriori Error Control for Conforming Mixed Approximations of Coercive Problems with Lower Order Terms.
- Authors
Anjam, Immanuel; Pauly, Dirk
- Abstract
The results of this contribution are derived in the framework of functional type a posteriori error estimates. The error is measured in a combined norm which takes into account both the primal and dual variables denoted by x and y, respectively. Our first main result is an error equality for all equations of the class or in mixed formulation , , where the exact solution is in . Here is a linear, densely defined and closed (usually a differential) operator and its adjoint. In this paper we deal with very conforming mixed approximations, i.e., we assume that the approximation belongs to . In order to obtain the exact global error value of this approximation one only needs the problem data and the mixed approximation itself, i.e., we have the equality where contains only known data. Our second main result is an error estimate for all equations of the class or in mixed formulation , , where i is the imaginary unit. For this problem we have the two-sided estimate where contains only known data. We will point out a motivation for the study of the latter problems by time discretizations or time-harmonic ansatz of linear partial differential equations and we will present an extensive list of applications including the reaction-diffusion problem and the eddy current problem.
- Publication
Computational Methods in Applied Mathematics, 2016, Vol 16, Issue 4, p609
- ISSN
1609-4840
- Publication type
Article
- DOI
10.1515/cmam-2016-0016