|Authors||M. E. Rognes and A. Logg|
|Title||Automated Goal-Oriented Error Control I: Stationary Variational Problems|
|Afilliation||Scientific Computing, , Scientific Computing|
|Project(s)||Center for Biomedical Computing (SFF)|
|Publication Type||Journal Article|
|Year of Publication||2013|
|Journal||SIAM Journal on Scientific Computing|
This article presents a general and novel approach to automated goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a\~posteriori error estimates, and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance. Numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented, including Poisson's equation, a mixed formulation of linear elasticity, and the incompressible Navier-Stokes equations.