p-version space-time least-squares finite-element method for unsteady convection-diffusion and Burgers' equations

A p-version-based space-time least-squares finite-element method (STLSFEM) is presented in this study. The method is applied to unsteady convection-diffusion and Burgers' equations which contain sharp gradients. Computed results demonstrates the stability, accuracy and efficiency of the present method for both linear and non-linear model problems. The method provides the basis for the extension of the space-time coupled least-squares minimization concept to multi-dimensional unsteady problems and appears to have great potential in computational fluid dynamics.