Locally conservative discontinuous Petrov-Galerkin finite elements for fluid problems
From MaRDI portal
Publication:2628399
DOI10.1016/j.camwa.2014.07.005zbMath1364.76086OpenAlexW2056321220MaRDI QIDQ2628399
Truman E. Ellis, Jesse Chan, Leszek F. Demkowicz
Publication date: 2 June 2017
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2014.07.005
Stokes flowadaptive mesh refinementconvection-diffusionleast squareslocal conservationhigher orderdiscontinuous Petrov-Galerkinminimum residual
PDEs in connection with fluid mechanics (35Q35) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
Related Items
Equivalence between the DPG method and the exponential integrators for linear parabolic problems ⋮ Local analysis of HDG methods for convection-dominated diffusion problems ⋮ A first order system least squares method for the Helmholtz equation ⋮ A DPG method for steady viscous compressible flow ⋮ Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid-thin structure interaction analysis, with application to heart valve modeling ⋮ Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation ⋮ Variational multiscale element free Galerkin (VMEFG) and local discontinuous Galerkin (LDG) methods for solving two-dimensional Brusselator reaction-diffusion system with and without cross-diffusion ⋮ To \(\mathcal{P}\) or not to \(p\) -- the mixed displacement-pressure \(p\), versus the higher order \(\mathcal{P}\) displacement finite element formulation, for nearly incompressible linear elasticity ⋮ A DPG method for the quad-curl problem ⋮ Weight-Adjusted Discontinuous Galerkin Methods: Wave Propagation in Heterogeneous Media ⋮ Robust DPG Methods for Transient Convection-Diffusion ⋮ A 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiers ⋮ A DPG method for planar div-curl problems ⋮ New periodic wave, cross-kink wave and the interaction phenomenon for the Jimbo-Miwa-like equation ⋮ An Algebraic Multigrid Method for an Adaptive Space–Time Finite Element Discretization ⋮ An analysis of discontinuous Galerkin methods for the compressible Euler equations: entropy and \(L_2\) stability ⋮ A High-Order Discontinuous Galerkin Solver for Helically Symmetric Flows ⋮ Isogeometric residual minimization method (iGRM) with direction splitting for non-stationary advection-diffusion problems ⋮ Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global \(L_2\) norm ⋮ A DPG-based time-marching scheme for linear hyperbolic problems ⋮ Isogeometric residual minimization (iGRM) for non-stationary Stokes and Navier-Stokes problems ⋮ Discrete least-squares finite element methods ⋮ High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations ⋮ Goal-Oriented Adaptive Mesh Refinement for Discontinuous Petrov--Galerkin Methods
Cites Work
- Unnamed Item
- A robust DPG method for convection-dominated diffusion problems. II: Adjoint boundary conditions and mesh-dependent test norms
- The DPG method for the Stokes problem
- A class of discontinuous Petrov-Galerkin methods. III: Adaptivity
- Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation
- A class of discontinuous Petrov-Galerkin methods. I: The transport equation
- A locking-free \(hp\) DPG method for linear elasticity with symmetric stresses
- On Bogovskiĭ and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains
- A DPG method for steady viscous compressible flow
- Robust DPG Method for Convection-Dominated Diffusion Problems
- An analysis of the practical DPG method
- A locally conservative, discontinuous least-squares finite element method for the Stokes equations
- Analysis of the DPG Method for the Poisson Equation
- Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
- Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
- Discrete Conservation Properties of Unstructured Mesh Schemes
- An Overview of the Discontinuous Petrov Galerkin Method