This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.
M.R. Baer and J.W. Nunziato . A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. J. Multiphase Flow, 12:861–889, 1986.
D. Balsara . Second-order accurate schemes for magnetohydrodynamics with divergence-free reconstruction. The Astrophysical Journal Supplement Series, 151:149–184, 2004.
D. Balsara and C.W. Shu . Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. Journal of Computational Physics, 160:405–452, 2000.
W. Boscheri , D.S. Balsara , and M. Dumbser . Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers. Journal of Computational Physics, 267:112–138, 2014.
W. Boscheri and M. Dumbser . A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D. Journal of Computational Physics, 275(0):484–523, 2014.
W. Boscheri and M. Dumbser . An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian-Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes. Journal of Scientific Computing, 66:240–274, 2016.
W. Boscheri , M. Dumbser , and D.S. Balsara . High Order Lagrangian ADER-WENO Schemes on Unstructured Meshes – Application of Several Node Solvers to Hydrodynamics and Magnetohydrodynamics. International Journal for Numerical Methods in Fluids, 76:737–778, 2014.
W. Boscheri , R. Loubère , and M. Dumbser . Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws. Journal of Computational Physics, 292:56–87, 2015.
M.J. Castro , J.M. Gallardo , J.A. López , and C. Parés . Well-balanced high order extensions of godunov's method for semilinear balance laws. SIAM Journal of Numerical Analysis, 46:1012–1039, 2008.
M.J. Castro , J.M. Gallardo , and C. Parés . High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. applications to shallow-water systems. Mathematics of Computation, 75:1103–1134, 2006.
S. Clain , S. Diot , and R. Loubère . A high-order finite volume method for systems of conservation lawsmulti-dimensional optimal order detection (MOOD). Journal of Computational Physics, 230(10):4028–4050, 2011.
Stéphane Clain , Gaspar J Machado , JM Nóbrega , and RMS Pereira . A sixth-order finite volume method for multidomain convection–diffusion problem with discontinuous coefficients. Computer Methods in Applied Mechanics and Engineering, 267:43–64, 2013.
B. Cockburn , G. E. Karniadakis , and C.W. Shu . Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering. Springer, 2000.
P. Colella and M.D. Sekora . A limiter for PPM that preserves accuracy at smooth extrema. Journal of Computational Physics, 227:7069–7076, 2008.
V. Deledicque and M.V. Papalexandris . An exact riemann solver for compressible two-phase flow models containing non-conservative products. Journal of Computational Physics, 222:217–245, 2007.
S. Diot , S. Clain , and R. Loubère . Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials. Computers and Fluids, 64:43–63, 2012.
S. Diot , R. Loubère , and S. Clain . The MOOD method in the three-dimensional case: Very-high-order finite volume method for hyperbolic systems. International Journal of Numerical Methods in Fluids, 73:362–392, 2013.
M. Dubiner . Spectral methods on triangles and other domains. Journal of Scientific Computing, 6:345–390, 1991.
M. Dumbser , D.S. Balsara , E.F. Toro , and C.-D. Munz . A unified framework for the construction of one-step finite volume and discontinuous galerkin schemes on unstructured meshes. Journal of Computational Physics, 227:8209–8253, 2008.
M. Dumbser and W. Boscheri . High-order unstructured Lagrangian one–step WENO finite volume schemes for non–conservative hyperbolic systems: Applications to compressible multi–phase flows. Computers and Fluids, 86:405–432, 2013.
M. Dumbser , M. Castro , C. Parés , and E.F. Toro . ADER schemes on unstructured meshes for non-conservative hyperbolic systems: Applications to geophysical flows. Computers and Fluids, 38:1731–1748, 2009.
M. Dumbser , C. Enaux , and E.F. Toro . Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. Journal of Computational Physics, 227:3971–4001, 2008.
M. Dumbser , A. Hidalgo , M. Castro , C. Parés , and E.F. Toro . FORCE schemes on unstructured meshes II: Non–conservative hyperbolic systems. Computer Methods in Applied Mechanics and Engineering, 199:625–647, 2010.
M. Dumbser , M. Kaeser , V.A. Titarev , and E.F. Toro . Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. Journal of Computational Physics, 226:204–243, 2007.
M. Dumbser and M. Käser . Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. Journal of Computational Physics, 221:693–723, 2007.
M. Dumbser and E. F. Toro . A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems. Journal of Scientific Computing, 48:70–88, 2011.
M. Dumbser , A. Uuriintsetseg , and O. Zanotti . On Arbitrary–Lagrangian–Eulerian One–Step WENO Schemes for Stiff Hyperbolic Balance Laws. Communications in Computational Physics, 14:301–327, 2013.
M. Dumbser and O. Zanotti . Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations. Journal of Computational Physics, 228:6991–7006, 2009.
S. Galera , P.H. Maire , and J. Breil . A two-dimensional unstructured cell-centered multi-material ale scheme using vof interface reconstruction. Journal of Computational Physics, 229:5755–5787, 2010.
A. Hidalgo and M. Dumbser . ADER schemes for nonlinear systems of stiff advection-diffusion-reaction equations. Journal of Scientific Computing, 48:173–189, 2011.
C. Hu and C.W. Shu . Weighted essentially non-oscillatory schemes on triangular meshes. Journal of Computational Physics, 150:97–127, 1999.
G.-S. Jiang and C.W. Shu . Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 126:202–228, 1996.
A.K. Kapila , R. Menikoff , J.B. Bdzil , S.F. Son , and D.S. Stewart . Two-phase modelling of DDT in granular materials: reduced equations. Physics of Fluids, 13:3002–3024, 2001.
M. Käser and A. Iske . ADER schemes on adaptive triangular meshes for scalar conservation laws. Journal of Computational Physics, 205:486–508, 2005.
P.M. Knupp . Achieving finite element mesh quality via optimization of the jacobian matrix normand associated quantities. part ii – a framework for volume mesh optimization and the condition number of the jacobian matrix. Int. J. Numer. Meth. Engng., 48:1165–1185, 2000.
Raphaël Loubère , Pierre-Henri Maire , Mikhail Shashkov , Jérôme Breil , and Stéphane Galera . Reale: A reconnection-based Arbitrary-Lagrangian-Eulerian method. J. Comput. Phys., 229(12):4724–4761, 2010.
P.H. Maire . A high-order cell-centered lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes. Journal of Computational Physics, 228:2391–2425, 2009.
P.H. Maire and B. Nkonga . Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics. Journal of Computational Physics, 228:799–821, 2009.
C. Olliver-Gooch and M. Van Altena . A high-order–accurate unstructured mesh finite–volume scheme for the advection–diffusion equation. Journal of Computational Physics, 181:729–752, 2002.
C. Parés . Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM Journal on Numerical Analysis, 44:300–321, 2006.
S. Rhebergen , O. Bokhove , and J.J.W. van der Vegt . Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations. Journal of Computational Physics, 227:1887–1922, 2008.
R. Saurel and R. Abgrall . A multiphase godunov method for compressible multifluid and multiphase flows. Journal of Computational Physics, 150:425–467, 1999.
D.W. Schwendeman , C.W. Wahle , and A.K. Kapila . The riemann problem and a high-resolution godunov method for a model of compressible two-phase flow. Journal of Computational Physics, 212:490–526, 2006.
A. Suresh and H.T. Huynh . Accurate monotonicity-preserving schemes with runge-kutta time stepping. Journal of Computational Physics, 136:83–99, 1997.
E.F. Toro . Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, second edition, 1999.
I. Toumi . A weak formulation of roes approximate riemann solver. Journal of Computational Physics, 102:360–373, 1992.
Alan M. Winslow . Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh. J. Comput. Phys., 135(2):128–138, August 1997.
P. Woodward and P. Colella . The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 54:115–173, 1984.
O. Zanotti , F. Fambri , and M. Dumbser . Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement. Mon. Not. R. Astron. Soc., 452:3010–3029, 2015.
Olindo Zanotti , Francesco Fambri , Michael Dumbser , and Arturo Hidalgo . Space-time adaptive ader discontinuous galerkin finite element schemes with a posteriori sub-cell finite volume limiting. Computers & Fluids, 118(0):204–224, 2015.