Spatial resolution in mixing processes is an acute problem. We propose a line method, akin to the contour dynamics technique, which is an extension of the particle method but with the particles redistributed on the line with time. We have used up to 105 particles per line and ten lines to investigate the dynamical and structural properties of mixing for both Newtonian and non-Newtonian temperature-dependent viscosity convection in 2D geometry. The spatial structures and the time history of the lines formed in Newtonian convection are different from those produced in non-Newtonian convection, which has the tendency for producing long-living horizontal structures. Efficient mixing in the upper mantle would be inhibited by non-Newtonian rheology.