A posteriori error estimates and adaptive finite elements for a nonlinear parabolic problem related to solidification Original Research Article

A posteriori error estimates are derived for a nonlinear parabolic problem arising from the isothermal solidification of a binary alloy. Space discretization with continuous, piecewise linear finite elements is considered. The L2 in time H1 in space error is bounded above and below by an error estimator based on the equation residual. Numerical results show that the effectivity index is close to one. An adaptive finite element algorithm is proposed and a solutal dendrite is computed.