Adjoint‐based error estimation and mesh adaptation for hybridized discontinuous Galerkin methods. (17th September 2014)

• Record Type: Journal Article
• Authors: Woopen, M.; May, G.; Schütz, J.
• Is Part Of: International journal for numerical methods in fluids. Volume 76:Number 11(2014:Dec.)
• Page Start: 811
• Page End: 834
• Publication Date: 2014-09-17
• Subjects: Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.3959
• Languages: English
• ISSNs: 0271-2091

Abstract

<abstract abstract-type="main" id="fld3959-abs-0001"> <title>Summary</title> <p id="fld3959-para-0001">We present a robust and efficient target‐based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection–diffusion problems, including the compressible Euler and Navier–Stokes equations. The hybridization of finite element discretizations has the main advantage that the resulting set of algebraic equations has globally coupled degrees of freedom (DOFs) only on the skeleton of the computational mesh. Consequently, solving for these DOFs involves the solution of a potentially much smaller system. This not only reduces storage requirements but also allows for a faster solution with iterative solvers. The mesh adaptation is driven by an error estimate obtained via a discrete adjoint approach. Furthermore, the computed target functional can be corrected with this error estimate to obtain an even more accurate value. The aim of this paper is twofold: Firstly, to show the superiority of adjoint‐based mesh adaptation over uniform and residual‐based mesh refinement and secondly, to investigate the efficiency of the global error estimate. Copyright © 2014 John Wiley &amp; Sons, Ltd.</p> </abstract>