Applications of a space-time FOSLS formulation for parabolic PDEs
arXiv:2208.09616 · doi:10.1093/imanum/drad012
Abstract
In this work, we show that the space-time first-order system least-squares (FOSLS) formulation [Führer, Karkulik, Comput. Math. Appl. 92 (2021)] for the heat equation and its recent generalization [Gantner, Stevenson, ESAIM Math. Model. Numer. Anal. 55 (2021)] to arbitrary second-order parabolic PDEs can be used to efficiently solve parameter-dependent problems, optimal control problems, and problems on time-dependent spatial domains.
References in corpus (8)
- Space-Time Isogeometric Analysis of Parabolic Evolution Equations
- A cut finite element method for coupled bulk-surface problems on time-dependent domains
- The Nitsche XFEM-DG space-time method and its implementation in three space dimensions
- Stability of Galerkin discretizations of a mixed space-time variational formulation of parabolic evolution equations
- Further results on a space-time FOSLS formulation of parabolic PDEs
- A Stable Space-Time Finite Element Method for Parabolic Evolution Problems
- Improved rates for a space-time FOSLS of parabolic PDEs
- A well-posed First Order System Least Squares formulation of the instationary Stokes equations