Abstract. Accurate simulation of glass melting furnaces requires the solution of very large linear algebraic systems of equations. To solve these equations efficiently a Schwarz domain decomposition (multi-block) method can be used. However, it can be observed that the convergence of the Schwarz method deteriorates when a large number of subdomains is used. This is due to small eigenvalues arising from the domain decomposition which slow down the convergence. Recently, a deflation approach was proposed to solve this problem using constant approximate eigenvectors. This paper generalizes this view to piecewise linear vectors and results for two CFD problems are presented. It can be observed that the number of iterations and wall clock time decrease considerably. The reason for this is that the norm of the initial residual is much smaller and the rate of convergence is higher.