BibTeX
@ARTICLE{
         Bucker2011SoD,
       author = "H. M. B{\"u}cker and E. Slusanschi",
       title = "Second-order Derivatives of the General-purpose Finite Element Package {SEPRAN} via
         Source Transformation",
       journal = "Mathematics and Computers in Simulation",
       issn = "0378-4754",
       pages = "2431--2439",
       doi = "10.1016/j.matcom.2011.03.008",
       abstract = "Second-order derivatives are crucial ingredients to a variety of numerical methods.
         Often, they are difficult to get with numerical differentiation by divided differencing. Automatic
         differentiation provides an alternative by a program transformation capable of evaluating Jacobians,
         Hessians, or higher-order derivatives of functions given in the form of computer programs. SEPRAN is
         a general-purpose finite element package written in Fortran~77 used in various scientific areas
         ranging from fluid dynamics to structural mechanics to electromagnetism. By transforming SEPRAN
         twice using the automatic differentiation tool ADIFOR, second-order derivatives are evaluated
         without truncation error. Numerical experiments are reported in which second-order derivatives of a
         flow field with respect to an inflow velocity are computed, demonstrating the feasibility of this
         approach.",
       year = "2011",
       volume = "81",
       number = "11",
       ad_tools = "ADIFOR",
       ad_theotech = "Hessian"
}