The finite element method provides a formalism for generating discrete (finite) algorithms for approximating the solutions of differential equations. It should be thought of as a black box into which one puts the differential equation (boundary value problem) and out of which pops an algorithm for approximating the corresponding solutions. Such a task could conceivably be done automatically by a computer, but it necessitates an amount of mathematical skill that today still requires human involvement. The purpose of this book is to help people become adept at working the magic of this black box. The book does not focus on how to turn the resulting algorithms into computer codes, but this topic is being pursued by several groups. In particular, the FEniCS project (on the web at fenics.org) utilizes the mathematical structure of the finite element method to automate the generation of finite element codes.
KeywordsBilinear Form Energy Norm Piecewise Linear Function Cantor Function Approximation Assumption
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