@Article{Alnaes:2014:UFL,
  author =       "Martin S. Aln{\ae}s and Anders Logg and Kristian B. {\O}lgaard and
                  Marie E. Rognes and Garth N. Wells",
  title =        "Unified Form Language: A Domain-Specific Language for Weak
                  Formulations of Partial Differential Equations",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume  =      40,
  number  =      2,
  year    =      2014,
  month   =      feb,
  pages =        "9:1--9:37",
  url =          "http://doi.acm.org/10.1145/2566630",
  accepted =     "22 April 2013",
  abstract =     "
                  We present the Unified Form Language (UFL), which
                  is a domain-specific language for representing weak
                  formulations of partial differential equations with
                  a view to numerical approximation. Features of UFL
                  include support for variational forms and functionals,
                  automatic differentiation of forms and expressions,
                  arbitrary function space hierarchies for multi-field
                  problems, general differential operators and flexible
                  tensor algebra. With these features, UFL has been
                  used to effortlessly express finite element methods
                  for complex systems of partial differential equations
                  in near-mathematical notation, resulting in compact,
                  intuitive and readable programs. We present in this work
                  the language and its construction. An implementation
                  of UFL is freely available as an open-source software
                  library. The library generates abstract syntax tree
                  representations of variational problems, which are used by
                  other software libraries to generate concrete low-level
                  implementations. Some application examples are presented
                  and libraries that support UFL are highlighted.",
}