Corners Give Problems When Decoupling Fourth Order Equations Into Second Order Systems

Abstract

Decoupling a fourth order elliptic boundary value problem into a system of second order equations may give an alternative approach to obtaining a solution for the original problem. The system approach is usually preferred for numerical methods since one may use piecewise linear finite elements to approximate a solution. In this note we compare both settings for the plate equation and prove that for planar domains with corners the system approach may fail to produce the correct solution.