The Statistical Finite Element Method
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The finite element method (FEM) is one of the great triumphs of modern day applied mathematics, numerical analysis and algorithm development. Engineering and the sciences benefit from the ability to simulate complex systems with FEM. At the same time the ability to obtain data by measurements from these complex systems, often through sensor networks, poses the question of how one systematically incorporates data into the FEM, consistently updating the finite element solution in the face of mathematical model misspecification with physical reality. This paper presents a statistical construction of FEM which goes beyond forward uncertainty propagation or solving inverse problems, and for the first time provides the means for the coherent synthesis of data and FEM.
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