A Posteriori Error Estimation Techniques for Finite Element Methods

Self-adaptive discretization methods nowadays are an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation. In this monograph we review the most frequently used a posteriori error estimation techniques and apply them to a broad class of linear and nonlinear elliptic and…