Object-Oriented Implementation of Field Recovery and Error Estimation in FEM

1. INTRODUCTION Computer programs for numerical solution of partial diierential equations are traditionally coded in the FORTRAN programming language. The computational intensive parts of such programs, either they are based on the nite 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 since it is particularly suitable for manipulation of large arrays. However, as the computers of today become more and more powerful and the compilers more and more eecient, the advantage of FORTRAN over alternative languages such as C and C++ are shrinking. Object-oriented programming techniques have therefore attracted an increasing popularity within the eld of numerical computing during the 90's, as such languages have predeened mechanisms for modular design, re-use of code and for creation of exible applications, etc. The present work is concerned with the use of object-oriented techniques in the development of a generic program module for a posteriori error estimation of FE computations. The program is written in C++ based on the Diipack framework 1]. The current version features recovery-based error estimation based on the superconvergent patch recovery (SPR) method 2]. The program is demonstrated on a two-dimensional linear elasticity problem. Since the SPR-method is well-known, the main focus is here put on the computational eeciency of the present implementation.