ANISOTROPIC MESH OPTIMIZATION AND ITS APPLICATION IN ADAPTIVITY

The construction of solution-adapted meshes is addressed within an opt imization framework. An approximation of the second spatial derivative of the solution is used to get a suitable metric in the computational domain. A mesh quality is proposed and optimized under this metric, a ccounting for both the shape and the size of the elements. For this pu rpose, a topological and geometrical mesh improvement method of high g enerality is introduced. It is shown that the adaptive algorithm that results recovers optimal convergence rates in singular problems, and t hat it captures boundary and internal layers in convection-dominated p roblems. Several important implementation issues are discussed. (C) 19 97 John Wiley & Sons, Ltd.