Error-constant estimation under the maximum norm for linear Lagrange interpolation

Abstract For the linear Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate error constant under maximum norm by using finite-element method (FEM). In solving optimization problem corresponding constant, in constraint condition is most difficult part process. To handle this difficulty, novel proposed combining orthogonality of space decomposition Fujino–Morley FEM and convex-hull property Bernstein representation functions space. Numerical results for lower upper bounds triangles various types are presented verify efficiency method.