Visualizing and displaying approximate solutions of PDEs on high resolution screens and other devices has become a significant part of scientific computation. On the other hand the prime focus of numerical analysts has been and still is on the development of effective numerical methods for generating accurate approximate solutions on relatively coarse meshes (covering the domain of interest). In order to display or visualize the results of such methods at the resolution required by the current display devices significant computational effort is often required and we are investigating efficient algorithms for carrying out these tasks.

In this presentation we will consider the efficient generation of contour plots and suface plots and the use of animation. We have developed and implemented (in MATLAB) an approach that directly generates surface plots and contour lines associated with a function $u(x,y)$ that does not have to solve a PDE on a fine mesh.

Our approach exploits knowledge of an underlying PDE to define a multivariate piecewise polynomial on a coarse unstructured mesh. This piecewise polynomial can then be used to generate accurate off-mesh data (in particular data required for effective visualization).We will show how this allows us to generate animated contour plots at a much lower cost than that involved in generating animated surface plots. Examples will be presented to show the effectiveness of this approach on a variety of realistic problems.