Hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Issue 4 (19th March 2014)

• Record Type: Journal Article
• Authors: Giani, Stefano; Houston, Paul
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 4(2014:Jul.)
• Page Start: 1342
• Page End: 1367
• Publication Date: 2014-03-19
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21872
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In this article, we develop the a posteriori error estimation of <italic>hp</italic>–version discontinuous Galerkin composite finite element methods for the discretization of second‐order elliptic partial differential equations. This class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or microstructures. Although standard numerical methods can be devised for such problems, the computational effort may be extremely high, as the minimal number of elements needed to represent the underlying domain can be very large. In contrast, the minimal dimension of the underlying composite finite element space is independent of the number of geometric features. Computable bounds on the error measured in terms of a natural (mesh‐dependent) energy norm are derived. Numerical experiments highlighting the practical application of the proposed estimators within an automatic <italic>hp</italic>–adaptive refinement procedure will be presented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1342–1367, 2014</p> </abstract>