An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
From MaRDI portal
Publication:481896
DOI10.1515/cmam-2014-0018zbMath1304.65248OpenAlexW1982576260MaRDI QIDQ481896
Alexandre Ern, Simon Lemaire, Daniele A. Di Pietro
Publication date: 18 December 2014
Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/cmam-2014-0018
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite volume methods for boundary value problems involving PDEs (65N08)
Related Items
Principles of a network element method ⋮ New polyhedral discretisation methods applied to the Richards equation: CDO schemes in \textit{Code\_Saturne} ⋮ A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method ⋮ A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation ⋮ Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids ⋮ The pursuit of a dream, Francisco Javier Sayas and the HDG methods ⋮ Hybrid high-order methods for finite deformations of hyperelastic materials ⋮ Refinement of polygonal grids using convolutional neural networks with applications to polygonal discontinuous Galerkin and virtual element methods ⋮ Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes ⋮ An advection-robust hybrid high-order method for the Oseen problem ⋮ Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods ⋮ Hybrid discretization methods with adaptive yield surface detection for Bingham pipe flows ⋮ An Arbitrary-Order Scheme on Generic Meshes for Miscible Displacements in Porous Media ⋮ Conservative polytopal mimetic discretization of the incompressible Navier-Stokes equations ⋮ A hybrid high-order method for the Sobolev equation ⋮ Superconvergent interpolatory HDG methods for reaction diffusion equations. II: HHO-inspired methods ⋮ Hybrid high-order methods for the acoustic wave equation in the time domain ⋮ A hybrid high-order method for Sobolev equation with convection-dominated term ⋮ HHO methods for the incompressible Navier-Stokes and the incompressible Euler equations ⋮ Design and analysis of the extended hybrid high-order method for the Poisson problem ⋮ Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches ⋮ Conditioning of a hybrid high-order scheme on meshes with small faces ⋮ \(p\)-multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation ⋮ An Unfitted Hybrid High-Order Method for Elliptic Interface Problems ⋮ A hybrid high-order locking-free method for linear elasticity on general meshes ⋮ An HDG method with orthogonal projections in facet integrals ⋮ Hybrid coupling of CG and HDG discretizations based on Nitsche's method ⋮ An a posteriori-driven adaptive mixed high-order method with application to electrostatics ⋮ Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes ⋮ A multigrid algorithm for the p-version of the virtual element method ⋮ A Staggered Discontinuous Galerkin Method of Minimal Dimension on Quadrilateral and Polygonal Meshes ⋮ A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes ⋮ Convergent adaptive hybrid higher-order schemes for convex minimization ⋮ Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods ⋮ An \(hp\)-hybrid high-order method for variable diffusion on general meshes ⋮ \(H^1, H(\text{curl})\) and \(H(\text{div})\) conforming elements on polygon-based prisms and cones ⋮ An arbitrary-order discrete de Rham complex on polyhedral meshes: exactness, Poincaré inequalities, and consistency ⋮ The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor ⋮ Weak Galerkin finite element with curved edges ⋮ Static Condensation, Hybridization, and the Devising of the HDG Methods ⋮ A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods ⋮ Discretization of Mixed Formulations of Elliptic Problems on Polyhedral Meshes ⋮ Discontinuous skeletal gradient discretisation methods on polytopal meshes ⋮ Superconvergence by $M$-decompositions. Part I: General theory for HDG methods for diffusion ⋮ The conforming virtual element method for polyharmonic problems ⋮ A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes ⋮ A brief review on polygonal/polyhedral finite element methods ⋮ Ws,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems ⋮ A hybrid high-order method for a coupled Stokes-Darcy problem on general meshes ⋮ Spectral approximation of elliptic operators by the Hybrid High-Order method ⋮ A Hybrid High-Order Method for Darcy Flows in Fractured Porous Media ⋮ A hybrid high-order method for the steady incompressible Navier-Stokes problem ⋮ High-order discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes ⋮ A hybrid high-order discretisation of the Brinkman problem robust in the Darcy and Stokes limits ⋮ A staggered DG method of minimal dimension for the Stokes equations on general meshes ⋮ A hybrid high-order method for incremental associative plasticity with small deformations ⋮ Mathematical and numerical modeling of plate dynamics with rotational inertia ⋮ A low-order nonconforming method for linear elasticity on general meshes ⋮ Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids ⋮ A high-order discontinuous Galerkin approach to the elasto-acoustic problem ⋮ Supercloseness of primal-dual Galerkin approximations for second order elliptic problems ⋮ Hybrid spectral difference methods for an elliptic equation ⋮ A Nyström-based finite element method on polygonal elements ⋮ Hybrid high-order methods for variable-diffusion problems on general meshes ⋮ A nonconforming Crouzeix-Raviart type finite element on polygonal meshes ⋮ An abstract analysis framework for monolithic discretisations of poroelasticity with application to hybrid high-order methods ⋮ A unified framework for high-order numerical discretizations of variational inequalities ⋮ Error estimation for the polygonal finite element method for smooth and singular linear elasticity ⋮ Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming ⋮ Assessment of hybrid high-order methods on curved meshes and comparison with discontinuous Galerkin methods ⋮ Convergence analysis of hybrid high-order methods for the wave equation ⋮ A hybrid high-order method for a class of quasi-Newtonian Stokes equations on general meshes ⋮ A polygonal discontinuous Galerkin method with minus one stabilization ⋮ Superconvergent interpolatory HDG methods for reaction diffusion equations. I: An \(HDG_k\) method ⋮ A Nonconforming High-Order Method for the Biot Problem on General Meshes ⋮ A hybrid high-order method for highly oscillatory elliptic problems ⋮ A discontinuous Galerkin method by patch reconstruction for convection-diffusion-reaction problems over polytopic meshes ⋮ A Hybrid High-Order Method for the Cahn--Hilliard problem in Mixed Form ⋮ Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods ⋮ Mixed virtual element methods for general second order elliptic problems on polygonal meshes ⋮ The nonconforming virtual element method ⋮ An H-Multigrid Method for Hybrid High-Order Discretizations ⋮ Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra ⋮ Superconvergent gradient recovery for virtual element methods ⋮ Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method ⋮ Hybrid high-order methods for the elliptic obstacle problem ⋮ High order exactly divergence-free Hybrid Discontinuous Galerkin methods for unsteady incompressible flows ⋮ A discontinuous skeletal method for the viscosity-dependent Stokes problem ⋮ Recovered finite element methods ⋮ A hybrid high-order method for the incompressible Navier-Stokes equations based on Temam's device ⋮ An arbitrary-order discontinuous Galerkin method with one unknown per element ⋮ Unfitted hybrid high-order methods for the wave equation ⋮ A hybrid high-order method for passive transport in fractured porous media ⋮ Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems ⋮ Hybrid coupling of finite element and boundary element methods using Nitsche's method and the calderon projection ⋮ Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and \(H^{1+r}, r>0\), regularity ⋮ A primal discontinuous Galerkin method with static condensation on very general meshes ⋮ A pressure robust staggered discontinuous Galerkin method for the Stokes equations ⋮ A p-robust polygonal discontinuous Galerkin method with minus one stabilization ⋮ Robust hybrid high-order method on polytopal meshes with small faces ⋮ Hybrid high-order method for singularly perturbed fourth-order problems on curved domains ⋮ A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem ⋮ Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem ⋮ Pressure robust hybrid mixed finite element method for Darcy–Forchheimer model ⋮ Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods ⋮ A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics ⋮ A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations ⋮ $hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes ⋮ A Hybrid High-Order Method for Quasilinear Elliptic Problems of Nonmonotone Type ⋮ A hybrid high‐order formulation for a Neumann problem on polytopal meshes ⋮ Hybridizable discontinuous Galerkin methods for second-order elliptic problems: overview, a new result and open problems ⋮ An immersed weak Galerkin method for elliptic interface problems on polygonal meshes ⋮ A polytopal method for the Brinkman problem robust in all regimes ⋮ Hybrid high-order methods for flow simulations in extremely large discrete fracture networks ⋮ Algebraic Multigrid Preconditioner for Statically Condensed Systems Arising from Lowest-Order Hybrid Discretizations ⋮ A posteriori error analysis of the hybrid high-order method for the Stokes problem ⋮ Surface tension effects between two immiscible Stokes fluids: a computational study using unfitted hybrid high-order methods and a level-set scheme ⋮ Stabilization-free HHO a posteriori error control ⋮ Agglomeration of polygonal grids using graph neural networks with applications to multigrid solvers ⋮ A semi‐hybrid‐mixed method for Stokes–Brinkman–Darcy flows with H(div)‐velocity fields ⋮ Trefftz Finite Elements on Curvilinear Polygons ⋮ A Skeletal High-Order Structure Preserving Scheme for Advection-Diffusion Equations ⋮ An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids ⋮ A hybrid high-order method for a class of strongly nonlinear elliptic boundary value problems ⋮ Time-explicit hybrid high-order method for the nonlinear acoustic wave equation ⋮ Interplay Between Diffusion Anisotropy and Mesh Skewness in Hybrid High-Order Schemes ⋮ A Three-Dimensional Hybrid High-Order Method for Magnetostatics ⋮ Preface ⋮ A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity ⋮ Staggered DG Methods for the Pseudostress-Velocity Formulation of the Stokes Equations on General Meshes ⋮ Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems ⋮ The Unfitted HHO Method for the Stokes Problem on Curved Domains ⋮ A Hybrid High-Order Method for Flow Simulations in Discrete Fracture Networks ⋮ A Hybrid High-Order Method for Multiple-Network Poroelasticity ⋮ A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation ⋮ Error estimate of the non-intrusive reduced basis method with finite volume schemes ⋮ Unnamed Item ⋮ A Sequential Least Squares Method for Poisson Equation Using a Patch Reconstructed Space ⋮ The nonconforming Virtual Element Method for eigenvalue problems ⋮ Anisotropic Error Estimates of the Linear Nonconforming Virtual Element Methods ⋮ Hybridized CutFEM for Elliptic Interface Problems ⋮ An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems ⋮ Optimal Maximum Norm Estimates for Virtual Element Methods
This page was built for publication: An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
