Object-oriented Field Recovery and Error Estimation in Finite Element Methods

In this chapter we study an object-oriented implementation of procedures for eld recovery and recovery-based error estimation. The eld recovery is based on the superconvergent patch recovery technique by Zienkiewicz and Zhu. The core of the current implementation is problem independent, and is organized as a set of C++ classes based on the software library Diipack. The use of the developed program module is demonstrated on an isotropic linear elasticity problem and on a stationary Navier{Stokes problem. For both example problems, analytical solutions are available. The exact error may therefore be computed in addition to the estimated error, enabling us to study the eeectivity of the estimator. The computational eeciency of the object-oriented program module is assessed by comparing the time consumption with a similar program implemented in FORTRAN. 1.1 Introduction Computer programs for numerical solution of Partial Diierential Equations (PDEs) are traditionally coded in the FORTRAN programming language. The computational intensive parts of such programs, based either on the Finite Element (FE) method or some other numerical procedure, consist mainly of various vector and matrix operations. FORTRAN has therefore been regarded as the best computer language for implementing these programs, as it is particularly suitable for manipulation of large arrays. However, as the computers of today become more and more powerful and the compilers more eecient, the advantage of FORTRAN over alternative languages such as C and C++ are shrinking. Moreover, the developments within the FE methods has by no means halted, as new procedures with