| This book resulted from lectures given at the University of Erlangen– Nuremberg and at the University of Magdeburg. On these occasions we often had to deal with the problem of a heterogeneous audience composed of students of mathematics and of different natural or engineering sciences.
Thus the expectations of the students concerning the mathematical accuracy and the applicability of the results were widely spread. On the other hand, neither relevant models of partial differential equations nor some knowledge of the (modern) theory of partial differential equations could be assumed among the whole audience. Consequently, in order to overcome the given situation, we have chosen a selection of models and methods relevant for applications (which might be extended) and attempted to illuminate the whole spectrum, extending from the theory to the implementation, without assuming advanced mathematical background. Most of the theoretical obstacles, difficult for nonmathematicians, will be treated in an “inductive” manner. In general, we use an explanatory style without (hopefully) compromising the mathematical accuracy.
We hope to supply especially students of mathematics with the information necessary for the comprehension and implementation of finite element/finite volume methods. For students of the various natural or engineering sciences the text offers, beyond the possibly already existing knowledge concerning the application of the methods in special fields, an introduction into the mathematical foundations, which should facilitate the transformation of specific knowledge to other fields of applications. |