A Stable Affine-Approximate Finite Element Method

摘要: The notion of the affine figure closest to a given quadrilateral can be precise mathematical definition. resulting is referred as equivalent parallelogram associated with quadrilateral. Equipped such concept, it then feasible consider finite element approximations in which original elements are replaced by their parallelograms. idea appealing, not least because economy arising from computations performed on an generated map. Furthermore, numerical experiments reported recently indicate that highly efficient and accurate schemes result when concept combined enhanced strain method or incompatible modes. purpose this work analyze approximation quadrilaterals focus low-order (bilinear) elements, analysis carried out context linear elasticity for standard well those use strains. applies only map, primary unknown (the displacement vector elasticity) approximated conventional piecewise bilinear functions. confirms convergence at optimal rate, provided deviations parallelograms most O(h).