On the circumradius condition for piecewise linear triangular elements
arXiv:1308.211321 citations
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For researchers in finite element methods, this refines the geometric conditions for convergence, but the result is incremental.
The paper argues that the circumradius condition is more essential than the maximum angle condition for convergence of the finite element method on triangular elements, and numerical experiments show it is optimal.
We discuss the error analysis of linear interpolation on triangular elements. We claim that the circumradius condition is more essential then the well-known maximum angle condition for convergence of the finite element method. Numerical experiments show that this condition is the best possible. We also point out that the circumradius condition is closely related to the definition of surface area.