OBJECT-ORIENTED PROGRAMMING OF ADAPTIVE FINITE-ELEMENT AND FINITE-VOLUME METHODS

This article describes an object-oriented implementation of the finite element method and the finite volume method in a unified adaptive sys tem using the programming language C++. The system applies to various types of mathematical model problems. Traditionally, different numeric al methods for different types of problems are implemented independent ly by procedural languages such as C and Fortran. Moreover, adaptive a nalysis programs are more complicated than nonadaptive programs. Never theless, these methods share many common properties such as linear sys tem solvers, data structures, a posteriori error analyses, and refinem ent processes. Some advantageous features of object-oriented programmi ng are demonstrated through the integration of these properties in the adaptive system. New data types of objects specific to adaptive metho ds are also introduced. The system is well-structured, extendable, and maintainable due mainly to the nature of encapsulation and inheritanc e of object-oriented programming.