Finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement
For researchers in computational geometry and finite element analysis, this work offers improved accuracy in curvature computation and mesh refinement, though it is incremental over existing techniques.
The paper develops stabilized finite element methods for computing mean curvature vectors and normals on triangulated surfaces, achieving first-order L2 convergence, and uses these to drive adaptive mesh refinement with spline-based surface reconstruction.
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 $L^2$-convergence of the mean curvature vector and apply this stabilization technique also to the computation of continuous, recovered, normals using $L^2$-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 or results to previously proposed approaches.