Convex hull property and maximum principle for finite element minimisers of general convex functionals

@article{Diening2013ConvexHP,
  title={Convex hull property and maximum principle for finite element minimisers of general convex functionals},
  author={Lars Diening and Christian Kreuzer and Sebastian Schwarzacher},
  journal={Numerische Mathematik},
  year={2013},
  volume={124},
  pages={685-700}
}
The convex hull property is the natural generalization of maximum principles from scalar to vector valued functions. Maximum principles for finite element approximations are often crucial for the preservation of qualitative properties of the respective physical model. In this work we develop a convex hull property for $$\mathbb{P }_1$$ conforming finite elements on simplicial non-obtuse meshes. The proof does not resort to linear structures of partial differential equations but directly… 

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