Anisotropic Mesh Adaptation Method, h-Variant
We discuss the construction of optimal meshes with respect to the interpolation error introduced in Chaps. 3 and 4. In particular, the goal is to construct a simplicial mesh such that the corresponding interpolation error is minimal, while the number of degrees of freedom is bounded from above. Alternatively, we seek a mesh such that the interpolation error is below a given tolerance, whereas the number of degrees of freedom is minimal. At the core of our approach is the continuous mesh formulation which allows one to use standard tools of variational calculus. Finally, we present an anisotropic mesh adaptation algorithm for the numerical solution of partial differential equations. Its performance is demonstrated by several numerical experiments. Here, we deal with the h-variant only, i.e., the polynomial degree of approximation is arbitrary but fixed. The extension to hp-adaptation is given in the next chapter.
