Maxwell eigenvalues and discrete compactness in two dimensions

✍ Scribed by L. Demkowicz; P. Monk; Ch. Schwab; L. Vardapetyan

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 833 KB
• Volume: 40
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(00)00182-6

✦ Synopsis

We present an elementary proof of the discrete compactness result for a general class of hp finite elements introduced in [1,2]. We discuss h-convergence of 2D elements only, and in this context, the results are not new as the analysis of H(curl)-conforming elements for Maxwell's equations can be reduced to the long-known results for Raviart-Thomas elements [3]. The work is based on the result of Kikuchi [4,5] for Nedelec's edge triangular elements of the lowest order and presents an alternative to techniques presented in [3,6]. In particular, the present version does not use an inverse inequality argument, and therefore, is valid for h-adaptive meshes. We conclude the presentation with a number of 2D computational experiments, including nonconvex domains. (~) 2000 Elsevier Science Ltd. All rights reserved.

Keywords--Maxwell's equations, hp finite elements. lWe shall refer to elements from [12] and [13] as the N@d@lec elements of the first or the second kind, respectively.