  A new anisotropic mesh adaptation strategy for finite element solution of
elliptic differential equations is presented. It generates anisotropic adaptive
meshes as quasi-uniform ones in some metric space, with the metric tensor being
computed based on a posteriori error estimates proposed in \cite{YinXie}. The
new metric tensor explores more comprehensive information of anisotropy for the
true solution than those existing ones. Numerical results show that this
approach can be successfully applied to deal with poisson and steady
convection-dominated problems. The superior accuracy and efficiency of the new
metric tensor to others is illustrated on various numerical examples of complex
two-dimensional simulations.
