387 RWTH Publication No: 230002        2014        IGPM387.pdf
TITLE Analysis of Trace Finite Element Methods for Surface Partial Differential Equations
AUTHORS Arnold Reusken
ABSTRACT 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
DOI 10.1093/imanum/dru047
PUBLICATION IMA Journal of Numerical Analysis 2015
35, 4, pp 1568-1590