We have performed phase-field simulations during directional solidification of a binary alloy. Adaptive mesh refinement techniques, in which the degrees of freedom of additional hanging nodes which occur when a quadrilateral element is refined are eliminated by matrix operations, are introduced to the finite element analysis in order to conduct the phase-field simulations efficiently. The validity of the numerical techniques presented here is ascertained by comparing the numerical results of the absolute stability limit and the onset of instability with those calculated from the Mullins-Sekerka theory and from the good linear relationship between log(P) and log(), in which the simulations under the constant concentration and temperature gradient are conducted by varying the pulling velocity. Furthermore, we examine the morphology change from cellular to dendritic structure and the relationship between log(;,) and log(G) for varying the temperature gradient. (c) 2005 Elsevier B.V. All rights reserved.