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Published in:
2021 | OriginalPaper | Chapter
1. Weak formulation of model problems
Authors : Alexandre Ern, Jean-Luc Guermond
Published in: Finite Elements II
Publisher: Springer International Publishing
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Abstract
This chapter presents a step-by-step derivation of weak formulations. We start by considering a few simple PDEs posed over a bounded domain, and we reformulate these problems in weak form using the important notion of test functions. We show by examples that there are many ways to write weak formulations. We consider second-order and first-order PDEs, and we also present an example for a complex-valued PDE. All of these problems can be cast into an abstract model problem.