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In this paper we consider finite element approaches to computing the meancurvature vector and normal at the vertices of piecewise linear triangulatedsurfaces. In particular, we adopt a stabilization technique which allows forfirst order $L^2$-convergence of the mean curvature vector and apply thisstabilization 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 refinementapproach to geometry resolution where we also employ spline techniques toreconstruct the surface before refinement. We compare or results to previouslyproposed approaches.

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