Mesh Smoothing Using A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
A Solution-Based Triangular and Tetrahedral Mesh Quality Indicator
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Metric tensors for anisotropic mesh generation
Journal of Computational Physics
Applied Numerical Mathematics - Applied scientific computing: Advances in grid generation, approximation and numerical modeling
Continuous metrics and mesh adaptation
Applied Numerical Mathematics
Continuous Mesh Framework Part II: Validations and Applications
SIAM Journal on Numerical Analysis
Continuous Mesh Framework Part II: Validations and Applications
SIAM Journal on Numerical Analysis
Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows
Journal of Computational Physics
Particle-based anisotropic surface meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Metric tensors for the interpolation error and its gradient in Lp norm
Journal of Computational Physics
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In the context of mesh adaptation, Riemannian metric spaces have been used to prescribe orientation, density, and stretching of anisotropic meshes. But, such structures are only considered to compute lengths in adaptive mesh generators. In this article, a Riemannian metric space is shown to be more than a way to compute a length. It is proven to be a reliable continuous mesh model. In particular, we demonstrate that the linear interpolation error can be evaluated continuously on a Riemannian metric space. From one hand, this new continuous framework proves that prescribing a Riemannian metric field is equivalent to the local control in the $\mathbf{L}^1$ norm of the interpolation error. This proves the consistency of classical metric-based mesh adaptation procedures. On the other hand, powerful mathematical tools are available and are well defined on Riemannian metric spaces: calculus of variations, differentiation, optimization$,\dots$, whereas these tools are not defined on discrete meshes.