AbstractWe extend an existing self-adaptive goal-oriented hp-adaptive Finite Element (FE) strategy to the case of multiple goals. The main idea of this extension is to design a new “quantity of interest” based on the solution of the direct problem and the given multiple goals. We describe an efficient implementation of the multigoal adaptive strategy, and we illustrate its performance with numerical results based on a time-harmonic electromagnetics model problem in two spatial dimensions (2D). Results illustrate the high accuracy and efficiency of our self-adaptive refinement strategy. The computational cost of our proposed multigoal-oriented adaptive strategy is similar to that of a single goal-oriented adaptive strategy. Multigoal oriented adaptive strategies are needed for a variety of engineering applications, including multiphysics and inverse problems in one, two, and three spatial dimensions.