On the Advantages and Drawbacks of A Posteriori Error Estimation for Fourth-Order Elliptic Problems

In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for the numerical solution of biharmonic and some further fourth order elliptic problems mostly in 2D. In the hp-adaptive finite element method, there are two possibilities to assess the error of the computed solution a posteriori: to construct a classical analytical error estimate or to obtain a more accurate reference solution by the same procedure as the approximate solution and, from it, the computational error estimate. For the lack of space, we sometimes only refer to the notation introduced in the papers quoted. The complete hypotheses and statements of the theorems presented should also be looked for there.