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SIAMNUM
2016

A Higher Order Finite Element Method for Partial Differential Equations on Surfaces

3 years 13 days ago
A Higher Order Finite Element Method for Partial Differential Equations on Surfaces
A new higher order finite element method for elliptic partial differential equations on a stationary smooth surface Γ is introduced and analyzed. We assume that Γ is characterized as the zero level of a level set function φ and only a finite element approximation φh (of degree k ≥ 1) of φ is known. For the discretization of the partial differential equation, finite elements (of degree m ≥ 1) on a piecewise linear approximation of Γ are used. The discretization is lifted to Γh, which denotes the zero level of φh, using a quasi-orthogonal coordinate system that is constructed by applying a gradient recovery technique to φh. A complete discretization error analysis is presented in which the error is split into a geometric error, a quadrature error, and a finite element approximation error. The main result is a H1(Γ)error bound of the form c(hm + hk+1). Results of numerical experiments illustrate the higher order convergence of this method. Key words. Laplace Beltrami e...
Jörg Grande, Arnold Reusken
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SIAMNUM
Authors Jörg Grande, Arnold Reusken
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