On the circumradius condition for piecewise linear triangular elements

摘要

We discuss the error analysis of linear interpolation on triangular elements.We claim that the circumradius condition is more essential then the well-knownmaximum angle condition for convergence of the finite element method. Numericalexperiments show that this condition is the best possible. We also point out that the circumradius condition is closely related to thedefinition of surface area.