Georg May

Journal article Journal of Computational Physics · November 1, 2025 In the context of increasing interest in space exploration, having a reliable means of predicting the behaviour of thermal protection material during atmospheric re-entry is of capital importance. Inductively coupled plasma facilities have been designed to ... Full text Cite

Towards a robust time-accurate anisotropically adaptive hybridized discontinuous Galerkin method

Journal article Computers and Fluids · October 30, 2025 Metric-based anisotropic mesh adaptation has proven effective for the solution of both steady and unsteady problems in terms of reduced computational time and accuracy gain. Especially for time-dependent problems, its generalization to implicit high-order ... Full text Cite

Conservative solution transfer between anisotropic meshes for time-accurate hybridized discontinuous Galerkin methods

Journal article International Journal for Numerical Methods in Fluids · June 1, 2024 We present a hybridized discontinuous Galerkin (HDG) solver for general time-dependent balance laws. In particular, we focus on a coupling of the solution process for unsteady problems with our anisotropic mesh refinement framework. The goal is to properly ... Full text Cite

Adjoint-based aerodynamic shape optimization with hybridized discontinuous Galerkin methods

Journal article Computers and Fluids · January 15, 2024 We present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for gene ... Full text Cite

Metric-based anisotropic mesh adaptation for viscoelastic flows

Journal article Computers and Mathematics with Applications · December 1, 2023 The computation of flows of viscoelastic fluids is expensive compared to standard fluids. Besides degrees-of-freedom for velocity and pressure, the viscoelastic stresses introduce an additional unknown to the system. While adaptive meshing techniques are c ... Full text Cite

A continuous hp-mesh model for discontinuous Petrov-Galerkin finite element schemes with optimal test functions

Journal article Computers and Mathematics with Applications · October 1, 2023 We present an anisotropic hp-mesh adaptation strategy using a continuous mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with optimal test functions, extending our previous work [1] on h-adaptation. The proposed strategy utilizes ... Full text Cite

An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control

Journal article Journal of Scientific Computing · May 1, 2023 We propose an efficient mesh adaptive method for the numerical solution of time-dependent partial differential equations considered in the fixed space-time cylinder Ω× (0 , T). We employ the space-time discontinuous Galerkin method which enables us to use ... Full text Cite

A review and comparison of error estimators for anisotropic mesh adaptation for flow simulations

Journal article Computers and Fluids · February 15, 2022 Automated mesh adaptation is known to be an efficient way to control discretization errors in Computational Fluid Dynamics (CFD) simulations. It offers the added advantage that the user only needs to have a minimal expertise in generating appropriate meshe ... Full text Cite

An anisotropic h-adaptive strategy for discontinuous Petrov-Galerkin schemes using a continuous mesh model

Journal article Computers and Mathematics with Applications · January 15, 2022 Certain Petrov-Galerkin schemes deliver inherently stable formulations of variational problems on a given mesh by selecting appropriate pairs of trial and test spaces. These schemes are especially suited for adaptation, due to their inherent ability to yie ... Full text Cite

Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods

Journal article Applied and Computational Mechanics · January 1, 2022 The present study is focused on the application of two families of implicit time-integration schemes for general time-dependent balance laws of convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely ba ... Full text Cite

A hybridized discontinuous galerkin solver for high-speed compressible flow

Journal article Aerospace · November 1, 2021 We present a high-order consistent compressible flow solver, based on a hybridized discontinuous Galerkin (HDG) discretization, for applications covering subsonic to hypersonic flow. In the context of high-order discretization, this broad range of applicat ... Full text Cite

Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model

Journal article Journal of Computational Physics · May 15, 2020 In this paper we propose an adjoint-based hp-adaptation method for conservation laws, and corresponding numerical schemes based on piecewise polynomial approximation spaces. The method uses a continuous mesh framework, similar to that proposed in [1], wher ... Full text Cite

A goal-oriented anisotropic hp-mesh adaptation method for linear convection–diffusion–reaction problems

Journal article Computers and Mathematics with Applications · November 1, 2019 We deal with the numerical solution of linear convection–diffusion–reaction equations using the hp-variant of the discontinuous Galerkin method on triangular grids. We develop a mesh adaptive algorithm which modifies the size and shape of mesh elements and ... Full text Cite

A goal-oriented high-order anisotropic mesh adaptation using discontinuous Galerkin method for linear convection-diffusion-reaction problems

Journal article SIAM Journal on Scientific Computing · January 1, 2019 We deal with the numerical solution of a linear convection-diffusion-reaction equation using the discontinuous Galerkin method of arbitrary polynomial approximation degree on anisotropic triangular grids. We derive a posteriori goal-oriented error estimate ... Full text Cite

A continuous hp-mesh model for adaptive discontinuous Galerkin schemes

Journal article Applied Numerical Mathematics · February 1, 2018 We present a continuous-mesh model for anisotropic hp-adaptation in the context of numerical methods using discontinuous piecewise polynomial approximation spaces. The present work is an extension of a previously proposed mesh-only (h-)adaptation method wh ... Full text Cite

Mesh optimization for discontinuous galerkin methods using a continuous mesh model

Journal article AIAA Journal · January 1, 2018 A method for anisotropic mesh adaptation and optimization for high-order discontinuous Galerkin schemes is presented. Given the total number of degrees of freedom, a metric-based method is proposed, which aims to globally optimize the mesh with respect to ... Full text Cite

Anisotropic hp-mesh optimization technique based on the continuous mesh and error models

Journal article Computers and Mathematics with Applications · July 1, 2017 We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the hp-version of the finite element method (hp-FEM). The technique uses a combination of approximation and interpolation error estimates to ... Full text Cite

Adjoint-based hp-adaptivity on anisotropic meshes for high-order compressible flow simulations

Journal article Computers and Fluids · November 5, 2016 We present an efficient adjoint-based hp-adaptation methodology on anisotropic meshes for high order Discontinuous Galerkin schemes applied to (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations. The refi ... Full text Cite

On the convergence of a shock capturing discontinuous galerkin method for nonlinear hyperbolic systems of conservation laws

Journal article SIAM Journal on Numerical Analysis · January 1, 2016 In this paper, we present a shock capturing discontinuous Galerkin method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time formulation in terms of entro ... Full text Cite

On the convergence of space-time discontinuous Galerkin schemes for scalar conservation laws?

Journal article SIAM Journal on Numerical Analysis · January 1, 2016 We prove convergence of a class of space-time discontinuous Galerkin schemes for scalar hyperbolic conservation laws. Convergence to the unique entropy solution is shown for all orders of polynomial approximation, provided strictly monotone flux functions ... Full text Cite

A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows

Journal article Journal of Scientific Computing · January 1, 2015 Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for compressible fluid flow. The extension of the multiresolution-based mesh adaptation concept to high-order discontinuous Galerkin disc ... Full text Cite

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

Journal article International Journal for Numerical Methods in Fluids · December 20, 2014 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 ... Full text Cite

A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow

Journal article Computers and Fluids · July 2, 2014 Objective: We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation for compressible flow problems. The aim is to provide a critical assessment of the computational efficiency ... Full text Cite

An adjoint consistency analysis for a class of hybrid mixed methods

Journal article IMA Journal of Numerical Analysis · January 1, 2014 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 Schütz and May (2013, AICES Technical Report ... Full text Cite

High-order CFD methods: Current status and perspective

Journal article International Journal for Numerical Methods in Fluids · July 20, 2013 After several years of planning, the 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7-8, 2012, just before the 50th Aerospace Sciences Meeting. The American Institute of Aeronautics and Astron ... Full text Cite

A hybrid mixed method for the compressible Navier-Stokes equations

Journal article Journal of Computational Physics · May 1, 2013 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 (DG) discretization for convection terms, and a Mixed me ... Full text Cite

A note on adjoint error estimation for one-dimensional stationary balance laws with shocks

Journal article SIAM Journal on Numerical Analysis · April 17, 2013 We consider one-dimensional steady-state balance laws with discontinuous solutions. Giles and Pierce [J. Fluid Mech., 426 (2001), pp. 327-345] realized that a shock leads to a new term in the adjoint error representation for target functionals. This term d ... Full text Cite

A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

Journal article Journal of Computational Physics · March 1, 2012 Numerical schemes using piecewise polynomial approximation are very popular for high order discretization of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Di ... Full text Cite

On the connection between the spectral difference method and the discontinuous Galerkin method

Journal article Communications in Computational Physics · January 1, 2011 In this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin (DG) discretization of a nonlinear conservation law. This allows interpretation of the Spectral Difference Scheme as a particular discretization unde ... Full text Cite

A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

Journal article Journal of Computational Physics · April 20, 2010 Higher order discretization has not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-practice relaxation techniques that compare favorably to ... Full text Cite

Spectral difference method for unstructured grids II: Extension to the Euler equations

Journal article Journal of Scientific Computing · July 1, 2007 An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve high-computatio ... Full text Cite

An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow

Journal article Journal of Computational Physics · January 10, 2007 During the past decade gas-kinetic methods based on the BGK simplification of the Boltzmann equation have been employed to compute fluid flow in a finite-difference or finite-volume context. Among the most successful formulations is the finite-volume schem ... Full text Cite