A least squares method for solving biharmonic problems

We discuss a generalization of the Cauchy Riemann equations, which is appli cable to biharmonic problems. A first-order system is derived from these eq uations, and this system is solved using the least squares method with cont inuous trial functions set up by the finite element method. Optimal rates o f convergence in L-2 (Omega) are proved in regions with smooth boundaries a nd optimal rates of convergence are proved in H-1 (Omega) and, using linear triangular elements, observed in L-2 (Omega) in polygonal regions.