Zlámal's minimum angle condition, a posteriori error estimation, averaging operators, conforming finite element method, discrete maximum principle, elliptic equation of fourth order, elliptic equation of second order, elliptic equations, elliptic system, error control in energy norm, error estimates of functional type, finite element method, higher order error estimates, local refinements, matrix irreducibility, maximum principles, mixed boundary conditions, monotone matrix, n-simplex, nested meshes, second order elasticity system, simplicial elements, strengthened Cauchy-Schwarz inequality, superconvergence, tetrahedral and prismatic elements.