Geodesic
On the evaluation of finite element sensitivities to nodal coordinates
Electronic transactions on numerical analysis, Tome 32 (2008), pp. 134-144.

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Summary: We present a derivation of the derivative of general systems of finite element equations with respect to the coordinates of the nodes in the underlying finite element mesh. The resulting expressions allow the systematic evaluation of such derivatives without the need to resort to automatic differentiation or the expense associated with finite difference approximations. The principal motivation for this work comes from problems in optimal design, however, other potential applications are also described. The results obtained are validated through numerical examples.
Classification : 65N30, 80M10, 49Q10, 49Q12
Keywords: adjoint, discrete adjoint, sensitivity analysis, differentiation, derivatives, finite element method, FEM, moving finite elements, moving mesh, moving nodes, nodal coordinates, node movement, node positions, shape derivative 
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     author = {Schneider, Ren\'e and Jimack, Peter K.},
     title = {On the evaluation of finite element sensitivities to nodal coordinates},
     journal = {Electronic transactions on numerical analysis},
     pages = {134--144},
     publisher = {mathdoc},
     volume = {32},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__32__a4/}
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Schneider, René; Jimack, Peter K. On the evaluation of finite element sensitivities to nodal coordinates. Electronic transactions on numerical analysis, Tome 32 (2008), pp. 134-144. http://geodesic.mathdoc.fr/item/ETNA_2008__32__a4/