A finite element method for surface diffusion: the parametric case

E Bänsch, P Morin, RH Nochetto - Journal of Computational Physics, 2005 - Elsevier
… In this paper, we consider the reduced purely geometric modelsurfaces or natural boundary
conditions for which integration by … Space adaptivity: accurate description of a surface with …

Finite elements on evolving surfaces

G Dziuk, CM Elliott - IMA journal of numerical analysis, 2007 - academic.oup.com
… define a new evolving surface finite-element method for numerically … geometry necessary
to describe the problem and numerical … We then obtain using integration by parts (2.2) and the …

The extended/generalized finite element method: an overview of the method and its applications

TP Fries, T Belytschko - … journal for numerical methods in …, 2010 - Wiley Online Library
… interface description is done in the real element geometry. For … We also note that the integration
of singular integrands is … [162], the integration on a crack surface with contact is discussed…

An adaptive stabilized trace finite element method for surface PDEs

T Heister, MA Olshanskii, V Yushutin - Computers & Mathematics with …, 2024 - Elsevier
… avoids integrationoverview of the motivation and the main results follow. At this point, we
will omit certain technical details regarding the geometrical consistency of the adaptive method

[PDF][PDF] Trace finite element method for material surface flows

A Zhiliakov - 2022 - uh-ir.tdl.org
… The map Ψ gives a Lagrangian description of the surface flow: a particle initially … the
geometrical evolution of the surface is known, ie, φ is prescribed and hence uN and all the geometric

[BOOK][B] The finite element method: basic concepts and applications

DW Pepper, JC Heinrich - 2005 - books.google.com
… the finite volume method, which is integrated), the governing equations in the finite element
method are integrated over each finite element … that allows us to describe the geometry of our …

An adaptive octree finite element method for PDEs posed on surfaces

AY Chernyshenko, MA Olshanskii - … Methods in Applied Mechanics and …, 2015 - Elsevier
… for the trace finite element method in H 1 and L 2 surface norms … order approximation of
curved geometries. It appears that the … , a problem of integration of finite element functions over Γ …

Multilevel reconstruction of visual surfaces: variational principles and finite-element representations

D Terzopoulos - Multiresolution image processing and analysis, 1984 - Springer
… the three-dimensional geometry of visible surfaces in a scene from … background of the finite
element method and the iterative … surface approximation problem has been posed in integral

A mixed quasi-trace surface finite element method for the Laplace-Beltrami problem

A Demlow - arXiv preprint arXiv:2309.12209, 2023 - arxiv.org
surface geometry and the mesh. In Section 3 we describe our finite element spaces and
method… In the first we defined all forms (integrals) needed in the method on the discrete surface Γ …

Numerical integration over implicitly defined domains for higher order unfitted finite element methods

MA Olshanskii, D Safin - Lobachevskii Journal of Mathematics, 2016 - Springer
… To define finite element methods, we need a formulation of the surface … with the finite element
interpolation and geometric error to … Reusken, “A trace finite element method for a class of …