Now showing items 1-7 of 7

    • A DPG-based time-marching scheme for linear hyperbolic problems 

      Muñoz-Matute, J.; Pardo, D.; Demkowicz, L. (2020-11)
      The Discontinuous Petrov-Galerkin (DPG) method is a widely employed discretization method for Partial Di fferential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time ...
    • Equivalence between the DPG method and the Exponential Integrators for linear parabolic problems 

      Muñoz-Matute, J.; Pardo, D.; Demkowicz, L. (2020-11)
      The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators are two well established numerical methods for solving Partial Di fferential Equations (PDEs) and sti ff systems of Ordinary Di fferential ...
    • Explicit-in-Time Goal-Oriented Adaptivity 

      Muñoz-Matute, J.; Calo, V.M.; Pardo, D.; Alberdi, E.; Van der Zee, K.G. (2019-04-15)
      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 ...
    • Explicit-in-Time Variational Formulations for Goal-Oriented Adaptivity 

      Muñoz-Matute, J. (2019-10)
      Goal-Oriented Adaptivity (GOA) is a powerful tool to accurately approximate physically relevant features of the solution of Partial Differential Equations (PDEs). It delivers optimal grids to solve challenging engineering ...
    • Forward-in-Time Goal-Oriented Adaptivity 

      Muñoz-Matute, J.; Pardo, D.; Calo, V.M.; Alberdi, E. (2019-03)
      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 ...
    • Time-Domain Goal-Oriented Adaptivity Using Pseudo-Dual Error Representations 

      Muñoz-Matute, J.; Alberdi, E.; Pardo, D.; Calo, V.M. (2017-12)
      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 ...
    • Variational Formulations for Explicit Runge-Kutta Methods 

      Muñoz-Matute, J.; Pardo, D.; Calo, V.M.; Alberdi, E. (2019-08)
      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 ...