Spectral Analysis of High Order Continuous FEM for Hyperbolic PDEs on Triangular Meshes: Influence of Approximation, Stabilization, and Time-Stepping

[1]  M. Ricchiuto,et al.  An efficient covariant frame for the spherical shallow water equations: Well balanced DG approximation and application to tsunami and storm surge , 2021, Ocean Modelling.

[2]  Mario Ricchiuto,et al.  Analytical travelling vortex solutions of hyperbolic equations for validating very high order schemes , 2021, ArXiv.

[3]  E. Burman Weighted Error Estimates for Transient Transport Problems Discretized Using Continuous Finite Elements with Interior Penalty Stabilization on the Gradient Jumps , 2021, Vietnam Journal of Mathematics.

[4]  R. Abgrall,et al.  Spectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and Time-Stepping , 2021, Journal of Scientific Computing.

[5]  Dmitri Kuzmin,et al.  Entropy stabilization and property-preserving limiters for ℙ1 discontinuous Galerkin discretizations of scalar hyperbolic problems , 2020, J. Num. Math..

[6]  Mats G. Larson,et al.  A cut finite element method for a model of pressure in fractured media , 2020, Numerische Mathematik.

[7]  Manuel Quezada de Luna,et al.  Entropy conservation property and entropy stabilization of high-order continuous Galerkin approximations to scalar conservation laws , 2020, Computers & Fluids.

[8]  Spencer J. Sherwin,et al.  Spatial eigenanalysis of spectral/hp continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity for high Reynolds number flows , 2020, J. Comput. Phys..

[9]  Sébastian Minjeaud,et al.  High Order CG Schemes for KdV and Saint-Venant Flows , 2020 .

[10]  Rémi Abgrall,et al.  High Order Asymptotic Preserving Deferred Correction Implicit-Explicit Schemes for Kinetic Models , 2020, SIAM J. Sci. Comput..

[11]  Rémi Abgrall,et al.  Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability , 2019, Communications on Applied Mathematics and Computation.

[12]  R. Abgrall,et al.  Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems , 2019, Journal of Scientific Computing.

[13]  D. Kuzmin,et al.  Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws , 2019, J. Comput. Phys..

[14]  Rémi Abgrall,et al.  Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes , 2019, J. Comput. Phys..

[15]  Philipp Offner,et al.  Arbitrary high-order, conservative and positivity preserving Patankar-type deferred correction schemes , 2019, Applied Numerical Mathematics.

[16]  Rémi Abgrall,et al.  High-order residual distribution scheme for the time-dependent Euler equations of fluid dynamics , 2018, Comput. Math. Appl..

[17]  F. Rapetti,et al.  Cubature Points Based Triangular Spectral Elements: an Accuracy Study , 2018, Journal of Mathematical Study.

[18]  Andrea Gilberto FILIPPINI,et al.  UHAINA : A parallel high performance unstructured near-shore wave model , 2018 .

[19]  Rémi Abgrall,et al.  High order methods for CFD , 2017 .

[20]  Rémi Abgrall,et al.  A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes , 2017, J. Comput. Phys..

[21]  Mats G. Larson,et al.  Stabilization of high order cut finite element methods on surfaces , 2017, IMA Journal of Numerical Analysis.

[22]  R. Abgrall,et al.  High Order Schemes for Hyperbolic Problems Using Globally Continuous Approximation and Avoiding Mass Matrices , 2017, J. Sci. Comput..

[23]  Francesca Rapetti,et al.  Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes , 2017, J. Comput. Phys..

[24]  Tao Xu,et al.  Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling , 2017, J. Comput. Phys..

[25]  Mrinal K. Sen,et al.  Dispersion analysis of the spectral element method using a triangular mesh , 2012 .

[26]  Jean-Luc Guermond,et al.  Entropy viscosity method for nonlinear conservation laws , 2011, J. Comput. Phys..

[27]  Miguel A. Fernández,et al.  Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems , 2010, SIAM J. Numer. Anal..

[28]  Benjamin Stamm,et al.  Interior Penalty Continuous and Discontinuous Finite Element Approximations of Hyperbolic Equations , 2010, J. Sci. Comput..

[29]  Thomas J. R. Hughes,et al.  Stabilized Methods for Compressible Flows , 2010, J. Sci. Comput..

[30]  Erik Burman,et al.  Consistent SUPG-method for transient transport problems: Stability and convergence , 2010 .

[31]  Santiago Badia,et al.  Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems , 2009, SIAM J. Numer. Anal..

[32]  Mario Ricchiuto,et al.  Stabilized residual distribution for shallow water simulations , 2009, J. Comput. Phys..

[33]  Stéphanie Salmon,et al.  Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping , 2007, Int. J. Appl. Math. Comput. Sci..

[34]  Francis X. Giraldo,et al.  A diagonal-mass-matrix triangular-spectral-element method based on cubature points , 2007 .

[35]  Steven J. Ruuth Global optimization of explicit strong-stability-preserving Runge-Kutta methods , 2005, Math. Comput..

[36]  John C. Butcher,et al.  Numerical Differential Equation Methods , 2005 .

[37]  P. Hansbo,et al.  Edge stabilization for Galerkin approximations of convection?diffusion?reaction problems , 2004 .

[38]  M. Minion Semi-implicit spectral deferred correction methods for ordinary differential equations , 2003 .

[39]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[40]  Roland Martin,et al.  WAVE PROPAGATION IN 2-D ELASTIC MEDIA USING A SPECTRAL ELEMENT METHOD WITH TRIANGLES AND QUADRANGLES , 2001 .

[41]  R. Codina Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods , 2000 .

[42]  Jean E. Roberts,et al.  Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation , 2000, SIAM J. Numer. Anal..

[43]  Mark A. Taylor,et al.  An Algorithm for Computing Fekete Points in the Triangle , 2000, SIAM J. Numer. Anal..

[44]  L. Greengard,et al.  Spectral Deferred Correction Methods for Ordinary Differential Equations , 2000 .

[45]  R. Codina,et al.  A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation , 1997 .

[46]  George Em Karniadakis,et al.  A triangular spectral element method; applications to the incompressible Navier-Stokes equations , 1995 .

[47]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[48]  ShuChi-Wang,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes, II , 1989 .

[49]  John J. H. Miller On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis , 1971 .

[50]  Jean-Luc Guermond,et al.  Stabilized Spectral Element Approximation of the Saint Venant System Using the Entropy Viscosity Technique , 2015 .

[51]  Benjamin Stamm,et al.  Stabilization Strategies for High Order Methods for Transport Dominated Problems , 2008 .

[52]  Peter Hansbo,et al.  The edge stabilization method for finite elements in CFD , 2003 .

[53]  Nathalie Tordjman,et al.  Éléments finis d'ordre élevé avec condensation de masse pour l'équation des ondes , 1994 .

[54]  J. Lambert Numerical Methods for Ordinary Differential Equations , 1991 .

[55]  J. Douglas,et al.  Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods , 1976 .