This work extends an automatic energy-norm $hp$-adaptive strategy based on performing quasi-optimal unrefinements to the case of non-elliptic problems and goal-oriented adaptivity. The proposed approach employs a multi-level ...

The main idea of our Goal-Oriented Adaptive (GOA) strategy is based on performing global and uniform h- or p-refinements (for h- and p-adaptivity, respectively) followed by a coarsening step, where some basis functions are ...

We present FCIRK16, a 16th-order implicit symplectic integrator for long-term high precision Solar System simulations. Our integrator takes advantage of the near-Keplerian motion of the planets around the Sun by ...

We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to ...

Solving inverse problems is a crucial task in several applications that strongly a ffect our daily lives, including multiple engineering fields, military operations, and/or energy production. There exist different methods ...

Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known ...

Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ...

In goal-oriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In time-dependent problems, this adaptive ...

Goal-oriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudo-dual problems for goal-oriented adaptivity in the ...