Abstract: In many practical problems that are modeled by PDEs, one is only interested in functional values, so-called goal values, derived from the solution of the PDE, e.g., the temperature or stress in some subdomain. We demonstrate how to design a goal-oriented adaptive FEM (GOAFEM) algorithm for linear elliptic PDEs, which drives down the error in the goal functional at optimal algebraic rate. Based on this adaptive algorithm, we present extensions to more practically relevant cases: nonlinear problems, inexact solution of the underlying FEM systems by an iterative solver, and PDE-based parameter estimation problems. Throughout, numerical experiments underline our theoretical findings.
Optimal goal-oriented adaptive FEM
30.03.2022 15:30 - 16:00
Organiser:
SFB 65, DK
Location:
Zoom Meeting
Related Files
- pde_afternoon_2022-03-30.pdf 491 KB