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The BR1 Scheme is Stable for the Compressible Navier–Stokes Equations
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An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction
Michael M. Crockatt, Andrew J. Christlieb, C. Kristopher Garrett and Cory D. Hauck Journal of Computational Physics 346 212 (2017) https://doi.org/10.1016/j.jcp.2017.06.017
A High-Order Time Domain Discontinuous Galerkin Method with Orthogonal Tetrahedral Basis for Electromagnetic Simulations in 3-D Heterogeneous Conductive Media
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High-order central Hermite WENO schemes: Dimension-by-dimension moment-based reconstructions
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Chi-Wang Shu Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 371 (2016) https://doi.org/10.1007/978-3-319-41640-3_12
A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals
A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin
Simone Marras, James F. Kelly, Margarida Moragues, et al. Archives of Computational Methods in Engineering 23(4) 673 (2016) https://doi.org/10.1007/s11831-015-9152-1
Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock
Jianming Liu, Jianxian Qiu, Mikhail Goman, Xinkai Li and Meilin Liu Numerical Mathematics: Theory, Methods and Applications 9(1) 87 (2016) https://doi.org/10.4208/nmtma.2015.m1416
A new approach for admissibility analysis of the direct discontinuous Galerkin method through Hilbert matrices
Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues
J. Qiu and Q. Zhang Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues 17 147 (2016) https://doi.org/10.1016/bs.hna.2016.06.001
Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
Recent Trends in Computational Engineering - CE2014
A. Beck, T. Bolemann, T. Hitz, V. Mayer and C.-D. Munz Lecture Notes in Computational Science and Engineering, Recent Trends in Computational Engineering - CE2014 105 281 (2015) https://doi.org/10.1007/978-3-319-22997-3_17
IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach
T. Bolemann, A. Beck, D. Flad, et al. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach 128 435 (2015) https://doi.org/10.1007/978-3-319-12886-3_20
A New Lax–Wendroff Discontinuous Galerkin Method with Superconvergence
The high order control volume discontinuous Petrov–Galerkin finite element method for the hyperbolic conservation laws based on Lax–Wendroff time discretization
A semi‐implicit, semi‐Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction
Giovanni Tumolo and Luca Bonaventura Quarterly Journal of the Royal Meteorological Society 141(692) 2582 (2015) https://doi.org/10.1002/qj.2544
Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement
IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach
T. Bolemann, M. Üffinger, F. Sadlo, T. Ertl and C. -D. Munz Notes on Numerical Fluid Mechanics and Multidisciplinary Design, IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach 128 535 (2015) https://doi.org/10.1007/978-3-319-12886-3_25
An Experimental and Numerical Study of Long Wave Run-Up on a Plane Beach
Ulrike Drähne, Nils Goseberg, Stefan Vater, Nicole Beisiegel and Jörn Behrens Journal of Marine Science and Engineering 4(1) 1 (2015) https://doi.org/10.3390/jmse4010001
Self-adjusting entropy-stable scheme for compressible Euler equations
Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data
A selective immersed discontinuous Galerkin method for elliptic interface problems
Xiaoming He, Tao Lin and Yanping Lin Mathematical Methods in the Applied Sciences 37(7) 983 (2014) https://doi.org/10.1002/mma.2856
An efficient parallel implementation of explicit multirate Runge–Kutta schemes for discontinuous Galerkin computations
Bruno Seny, Jonathan Lambrechts, Thomas Toulorge, Vincent Legat and Jean-François Remacle Journal of Computational Physics 256 135 (2014) https://doi.org/10.1016/j.jcp.2013.07.041
A fully discrete local discontinuous Galerkin method for one-dimensional time-fractional Fisher's equation
High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations
Andrea D. Beck, Thomas Bolemann, David Flad, Hannes Frank, Gregor J. Gassner, Florian Hindenlang and Claus‐Dieter Munz International Journal for Numerical Methods in Fluids 76(8) 522 (2014) https://doi.org/10.1002/fld.3943
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
A Review of Recent Advances in Discretization Methods,a PosterioriError Analysis, and Adaptive Algorithms for Numerical Modeling in Geosciences
Daniele A. Di Pietro and Martin Vohralík Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 69(4) 701 (2014) https://doi.org/10.2516/ogst/2013158
Alternating evolution discontinuous Galerkin methods for Hamilton–Jacobi equations
Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations
Chi-Wang Shu The IMA Volumes in Mathematics and its Applications, Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations 157 25 (2014) https://doi.org/10.1007/978-3-319-01818-8_2
A uniformly second order fast sweeping method for eikonal equations