An Adjoint Consistency Analysis for a Class of Hybrid Mixed Methods

@article{Schtz2014AnAC,
  title={An Adjoint Consistency Analysis for a Class of Hybrid Mixed Methods},
  author={Jochen Sch{\"u}tz and Georg May},
  journal={Ima Journal of Numerical Analysis},
  year={2014},
  volume={34},
  pages={1222-1239}
}
  • J. SchützG. May
  • Published 1 July 2014
  • Computer Science
  • Ima Journal of Numerical Analysis
Hybrid methods represent a classic discretization paradigm for elliptic equations. More recently, hybrid methods have been formulated for convection-diffusion problems, in particular compressible fluid flow. In [25], we have introduced a hybrid mixed method for the compressible Navier-Stokes equations as a combination of a hybridized DG scheme for the convective terms, and an H(div,Ω)-method for the diffusive part. Since hybrid methods are based on Galerkin’s principle, the adjoint of a given… 

A Combined Hybridized Discontinuous Galerkin / Hybrid Mixed Method For Viscous Conservation Laws

This paper extends their method to be able to cope with time-dependent convection-diffusion equations, where they use a dual time-stepping method in combination with backward difference schemes.

Hp-Adaptivity on Anisotropic Meshes for Hybridized Discontinuous Galerkin Scheme

We present an efficient adaptation methodology on anisotropic meshes for the recently developed hybridized discontinuous Galerkin scheme for (nonlinear) convection-diffusion problems, including

Adjoint-Based Hp-Adaptation for a Class of High-Order Hybridized Finite Element Schemes for Compressible Flows

We present a robust and efficient hp-adaptation methodology, building on a class of hybridized finite element schemes for (nonlinear) convection-diffusion problems, including compressible Euler and

A Hybridized Discontinuous Galerkin Method for Unsteady Flows with Shock-Capturing

A hybridized discontinuous Galerkin (HDG) solver for the time-dependent compressible Euler and Navier-Stokes equations is presented, and adaptive time stepping using an embedded error estimator is employed.

Adjoint‐based error estimation and mesh adaptation for hybridized discontinuous Galerkin methods

We present a robust and efficient target‐based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection–diffusion problems, including the

A Hybridized Discontinuous Galerkin Method for Three-Dimensional Compressible Flow Problems

A hybridized discontinuous Galerkin method for three-dimensional flow problems that allows for a faster solution with iterative solvers, and is validated with a scalar convection-diffusion test case.

Hybridized Discontinuous Galerkin Methods for Wave Propagation

This work presents the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism, which are amenable to hybridization (static condensation) and hence to more efficient implementations.

A Hybridized Discontinuous Galerkin Solver for High-Speed Compressible Flow

A high-order consistent compressible flow solver, based on a hybridized discontinuous Galerkin (HDG) discretization, for applications covering subsonic to hypersonic flow and the implementation of flexible modeling using object-oriented programming and algorithmic differentiation is presented.

Hybridisable Discontinuous Galerkin Formulation of Compressible Flows

An original unified framework for the derivation of Riemann solvers in hybridised formulations is proposed and includes, for the first time in an HDG context, the HLL and HLLEM Riem Mann solvers as well as the traditional Lax–Friedrichs and Roe solvers.

References

SHOWING 1-10 OF 34 REFERENCES

A hybrid mixed discontinuous Galerkin finite-element method for convection–diffusion problems

We propose and analyse a new finite-element method for convection―diffusion problems based on the combination of a mixed method for the elliptic and a discontinuous Galerkin (DG) method for the

A Hybridized DG/Mixed Scheme for Nonlinear Advection-Diffusion Systems, Including the Compressible Navier-Stokes Equations

We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin

A hybrid mixed finite element scheme for the compressible Navier-Stokes equations and adjoint-based error control for target functionals

The importance of computer-based modeling in technical and industrial use is evident. Especially the aerodynamic industry has a huge interest in reliable and robust methods for accurately computing

A Hybridizable Discontinuous Galerkin Method for the Compressible Euler and Navier-Stokes Equations

The HDG method inherits the geometric flexibility and arbitrary high order accuracy of Discontinuous Galerkin methods, but offers a significant reduction in the computational cost as well as improved accuracy and convergence properties.

Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations

A general framework for analyzing the adjoint consistency of DG discretizations is provided which is useful for the derivation of adjoint consistent methods and the link to the accuracy of numerical flow solutions and the smoothness of discrete adjoint solutions is demonstrated.

Analysis of Dual Consistency for Discontinuous Galerkin Discretizations of Source Terms

Numerical results for a one-dimensional test problem confirm that the dual consistent and asymptotically dual consistent schemes achieve higher asymPTotic convergence rates with grid refinement than a similar dual inconsistent scheme for both the primal and adjoint solutions as well as a simple functional output.

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

A unifying framework for hybridization of finite element methods for second order elliptic problems is introduced, thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques, as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom.

A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations

This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier?Stokes equations. We extend a discontinuous finite element

The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multi-D systems

The algorithm formulation and practical implementation issues such as the numerical fluxes, quadrature rules, degrees of freedom, and the slope limiters are discussed, both in the triangular and the rectangular element cases.