Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement

A new adjoint sensitivity analysis approach is presented for time-dependent partial differential equations with adaptive mesh refinement. The new approach, called ADDA, combines the best features of both the adjoint of the discretization (AD) and discretization of the adjoint (DA) approaches. It removes the obstacles of applying AD to adaptive methods and, in contrast to DA, requires for its use only a minimal amount of knowledge about the formulation of adjoint PDEs and their boundary conditions. The effectiveness and efficiency of ADDA are demonstrated for several numerical examples.