Finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement

• In this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces. In particular, we adopt a stabilization technique which allows for first order L2-convergence of the mean curvature vector and apply this stabilization technique also to the computation of continuous, recovered, normals using L2-projections of the piecewise constant face normals. Finally, we use our projected normals to define an adaptive mesh refinement approach to geometry resolution where we also employ spline techniques to reconstruct the surface before refinement. We compare our results to previously proposed approaches.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datorteknik (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Engineering (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Continuous interior penalty

Discrete curvature

Finite element method

Projection method

Piecewise linear techniques

Stabilization

Adaptive mesh refinement

Finite element procedure

Finite-element approach

Mean curvature vector

Piece-wise constants

Piecewise linear

Stabilization techniques

Triangulated surfaces

Mesh generation

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)