| Abstract: | Solutions of partial differential equations (PDEs) using globally nonvanishing approximating functions are discussed, and the particular case of global polynomial solutions is studied. Convergence and error bounds are examined. Examples are given and compared with analytic solutions. This method seems particularly well suited for elliptic PDEs with continuous boundary conditions and nonhomogeneous terms, even for irregular domains, offering geometric convergence rates. By providing the minimized residues, strong error indicators are obtained. This algorithm's implementation retains simplicity under a variety of applications. |
