LOCAL ANISOTROPIC INTERPOLATION ERROR ESTIMATES BASED ON DIRECTIONAL DERIVATIVES ALONG EDGES

摘要

We present new local anisotropic error estimates for the Lagrangian finite element interpolation. The bounds apply to affine equivalent elements and use information from directional derivatives of the function to interpolate along a set of adjacent edges. These new bounds do not require any geometric limitation but may vary, in some cases, with the node ordering. Several existing results are recovered from the new bounds. Examples compare the asymptotic behavior of the new and existing bounds when the diameter of the element goes to zero. For some elements with small or large angles, our new bound exhibits the same asymptotic behavior as the norm of the interpolation error while existing results do not have the correct asymptotic behavior.