DISCONTINUOUS GALERKIN METHODS FOR FIRST-ORDER HYPERBOLIC PROBLEMS

From MaRDI portal

Publication:4678337

Jump to:navigation, search

DOI10.1142/S0218202504003866zbMath1070.65117OpenAlexW2125822172WikidataQ57386747 ScholiaQ57386747MaRDI QIDQ4678337

Franco Brezzi, Endre Süli, Luisa Donatella Marini

Publication date: 23 May 2005

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202504003866

zbMATH Keywords

stability error estimates first-order hyperbolic problems discontinuous Galerkin methods upwinding linear hyperbolic equations advection-dominated equations jump stabilizations

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Initial-boundary value problems for first-order hyperbolic systems (35L50)

Related Items (82)

Discontinuous Galerkin solution of a phase-field model in isothermal chemical vapor infiltration of SiC ⋮ Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows ⋮ A short note on the accuracy of the discontinuous Galerkin method with reentrant faces ⋮ Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation ⋮ Output error estimation strategies for discontinuous Galerkin discretizations of unsteady convection-dominated flows ⋮ A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and \(\operatorname{div} B = 0\) ⋮ On streamline diffusion schemes for the one and one-half dimensional relativistic Vlasov-Maxwell system ⋮ Error analysis of piecewise constant pressure approximations of Darcy's law ⋮ Discontinuous Galerkin finite element approximation of the two‐dimensional Navier–Stokes equations in stream‐function formulation ⋮ An advection-robust hybrid high-order method for the Oseen problem ⋮ Discontinuous Galerkin Methods for Linear Problems: An Introduction ⋮ Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains ⋮ Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces ⋮ Stabilization mechanisms in discontinuous Galerkin finite element methods ⋮ A hybridized discontinuous Galerkin method on mapped deforming domains ⋮ Discontinuous Galerkin method for piecewise regular solutions to the nonlinear age-structured population model ⋮ Stabilized discontinuous Galerkin methods for scalar linear hyperbolic equations ⋮ On Local Super-Penalization of Interior Penalty Discontinuous Galerkin Methods ⋮ Battling Gibbs phenomenon: on finite element approximations of discontinuous solutions of PDEs ⋮ A simple finite element method for linear hyperbolic problems ⋮ Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law ⋮ Adaptive least-squares finite element methods for linear transport equations based on an H(div) flux reformulation ⋮ Analytical and variational numerical methods for unstable miscible displacement flows in porous media ⋮ Stabilised DG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes ⋮ Compatible finite element methods for geophysical fluid dynamics ⋮ Discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints ⋮ Discontinuous Galerkin methods based on weighted interior penalties for second order PDEs with non-smooth coefficients ⋮ Interior penalty continuous and discontinuous finite element approximations of hyperbolic equations ⋮ A hybrid discontinuous in space and time Galerkin method for wave propagation problems ⋮ A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations ⋮ Jump penalty stabilization techniques for under-resolved turbulence in discontinuous Galerkin schemes ⋮ Investigation of commutative properties of discontinuous Galerkin methods in PDE constrained optimal control problems ⋮ Stabilized cut discontinuous Galerkin methods for advection-reaction problems on surfaces ⋮ A locking-free discontinuous Galerkin method for linear elastic Steklov eigenvalue problem ⋮ Families of hybridized interior penalty discontinuous Galerkin methods for locally degenerate advection-diffusion-reaction problems ⋮ A scalable DG solver for the electroneutral Nernst-Planck equations ⋮ Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: discrete divergence operator ⋮ An \(L^p\)-primal-dual finite element method for first-order transport problems ⋮ A robust \(S_{N}\)-DG-approximation for radiation transport in optically thick and diffusive regimes ⋮ Computing gravity-driven viscous fingering in complex subsurface geometries: a high-order discontinuous Galerkin approach ⋮ Convergence of lowest-order semi-Lagrangian schemes ⋮ Bubble stabilization of discontinuous Galerkin methods ⋮ Stabilized Cut Discontinuous Galerkin Methods for Advection-Reaction Problems ⋮ A posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems ⋮ On \(hp\)-streamline diffusion and Nitsche schemes for the relativistic Vlasov-Maxwell system ⋮ A new upwind weak Galerkin finite element method for linear hyperbolic equations ⋮ Minimal stabilization for discontinuous Galerkin finite element methods for hyperbolic problems ⋮ Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection-diffusion-reaction problems ⋮ Numerical error analysis for an energy-stable HDG method for the Allen-Cahn equation ⋮ A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model ⋮ Streamline diffusion method for treating coupling equations of hyperbolic scalar conservation laws ⋮ A space-time discontinuous Galerkin method for the time-dependent Oseen equations ⋮ DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM ⋮ A novel hybrid difference method for an elliptic equation ⋮ Discontinuous Galerkin method for the solution of a transport level-set problem ⋮ High-order discontinuous Galerkin methods for a class of transport equations with structured populations ⋮ Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian grids ⋮ Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations ⋮ Stability and error analysis of mixed finite-volume methods for advection dominated problems ⋮ A Sparse Grid Discrete Ordinate Discontinuous Galerkin Method for the Radiative Transfer Equation ⋮ Output-based space-time mesh adaptation for the compressible Navier-Stokes equations ⋮ Mixed discontinuous Galerkin methods for Darcy flow ⋮ Optimal error estimate and superconvergence of the DG method for first-order hyperbolic problems ⋮ Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case ⋮ Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm ⋮ On discrete maximum principles for discontinuous Galerkin methods ⋮ Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs ⋮ Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions ⋮ Shock capturing techniques for \(h p\)-adaptive finite elements ⋮ An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms ⋮ Differentiable monotonicity-preserving schemes for discontinuous Galerkin methods on arbitrary meshes ⋮ A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations ⋮ A conservative finite element method for the incompressible Euler equations with variable density ⋮ High order discontinuous cut finite element methods for linear hyperbolic conservation laws with an interface ⋮ Approximation of the multi-dimensional incompressible Navier-Stokes equations by discrete-velocity vector-BGK models ⋮ Nonsymmetric Reduction-Based Algebraic Multigrid ⋮ Convergence in Norm of Nonsymmetric Algebraic Multigrid ⋮ Weighted error estimates for transient transport problems discretized using continuous finite elements with interior penalty stabilization on the gradient jumps ⋮ On Fixed-Point, Krylov, and $2\times 2$ Block Preconditioners for Nonsymmetric Problems ⋮ Analysis of a Combined CG1-DG2 Method for the Transport Equation ⋮ Staggered-grid spectral element methods for elastic wave simulations ⋮ Stabilized Galerkin for transient advection of differential forms

Cites Work

This page was built for publication: DISCONTINUOUS GALERKIN METHODS FOR FIRST-ORDER HYPERBOLIC PROBLEMS

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:4678337&oldid=18898861"