Control of geometry induced error in hp finite element (FE) simulations, I. Evaluation of FE error for curvilinear geometries
Dong Xue 1, Leszek Demkowicz 21 Department of Engineering Mechanics, University of Texas at Austin, TX, 78712, USA
2 Institute of Computational Engineering and Science, University of Texas at Austin, TX, 78712, USA
Received by the editors October 13, 2003 and, in revised form, March 22, 2004
The paper discusses a general framework for handling curvilinear geometries in high accuracy Finite Element (FE) simulations, for both elliptic and Maxwell problems. Based on the differential manifold concept, the domain is represented as a union of geometrical blocks prescribed with globally compatible, explicit or implicit parametrizations. The idea of parametric H-1-, H(curl)- and H(div) - conforming elements is reviewed, and the concepts of exact geometry elements and isoparametric elements are discussed. The paper focuses then on isoparametric elements, and two ways of computing FE discretization errors: a popular one, neglecting the geometry approximation, and a precise one, utilizing the exact geometry representation. Presented numerical examples indicate the necessity of accounting for the geometry error in FE error calculations., especially for the H(curl) problems.
AMS subject classifications: 35R35, 49J40, 60G40
Key words: geometry approximation; curvilinear hp Finite Element(FE) meshes; error evaluation; Exact Geometry Integration (EGI)
Email: firstname.lastname@example.org (D. Xue), email@example.com (L. Demkowicz)