|Preprint-No.:||< 387 >||Published in:||March 2014||PDF-File:||IGPM387.pdf|
|Title:||Analysis of Trace Finite Element Methods for Surface Partial Differential Equations|
In this paper we consider two variants of a trace ﬁnite element method for solving elliptic partial differential equations on a stationary smooth manifold Γ. A discretization error analysis for both methods in one general framework is presented. Higher order ﬁnite elements are treated and rather general numerical approximations Γh of the manifold Γ are allowed. Optimal order discretization error bounds are derived. Furthermore, the conditioning of the stiffness matrices is studied. It is proved that for one of these two variants the corresponding scaled stiffness matrix has a condition number ∼ h−2, independent of how Γh intersects the outer triangulation.
|Keywords:||trace ﬁnite elements, error analysis, elliptic surface equation|
|Publication:||IMA Journal of Numerical Analysis 2015 |
35, 4, 1568-1590