A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains. Issue 1 (12th June 2018)

• Record Type: Journal Article
• Authors: Constantinou, P.; Franz, S.; Ludwig, L.; Xenophontos, C.
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 1(2019)
• Page Start: 114
• Page End: 127
• Publication Date: 2018-06-12
• Subjects: boundary layers -- fourth‐order singularly perturbed problem -- mixed hp finite element method -- spectral boundary layer mesh -- uniform exponential convergence; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22289
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed h p Finite Element Method on the so‐called Spectral Boundary Layer Mesh . We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.