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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the discrete exterior calculus (DEC) or finite element exterior calculus (FEEC) is the extension to the method of finite elements of the exterior calculus of differentiable manifolds. DEC methods have proved to be very powerful in improving and analyzing finite element methods: for instance, DEC-based methods allow the use of highly non-uniform meshes to obtain accurate results. Non-uniform meshes are advantageous because they allow the use of large elements where the process to be simulated is relatively simple, as opposed to a fine resolution where the process may be complicated (e.g., near an obstruction to a fluid flow), while using less computational power than if a uniformly fine mesh were used.