A C0 interior penalty method for a singularly‐perturbed fourth‐order elliptic problem on a layer‐adapted mesh. Issue 3 (14th December 2013)

• Record Type: Journal Article
• Authors: Franz, Sebastian; Roos, Hans‐Görg; Wachtel, Andreas
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 3(2014:May)
• Page Start: 838
• Page End: 861
• Publication Date: 2013-12-14
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21839
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>We analyze the convergence of a continuous interior penalty (CIP) method for a singularly perturbed fourth‐order elliptic problem on a layer‐adapted mesh. On this anisotropic mesh, we prove under reasonable assumptions uniform convergence of almost order <italic>k</italic> − 1 for finite elements of degree <italic>k</italic> ≥ 2. This result is of better order than the known robust result on standard meshes. A by‐product of our analysis is an analytic lower bound for the penalty of the symmetric CIP method. Finally, our convergence result is verified numerically. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 838–861, 2014</p> </abstract>