Multigoal-oriented adaptive finite element methods with convergence rates

Abstract We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation that can simultaneously deal with $$2 \le N$$ 2 ≤ N linear goal functionals. In each adaptive step, the proposed algorithm requires only to solve two linear finite element systems. Moreover, all finite element solutions are computed with respect to the same discrete space, while the underlying triangulations are adapted to resolve all inherent singularities simultaneously. Unlike available results for multigoal-oriented adaptive finite element methods in the literature, we give the first thorough convergence analysis and prove that our algorithm guarantees, in the usual sense, even optimal convergence rates. Numerical experiments underline the derived theoretical results.