Efficient rectangular mixed finite elements in two and three space variables
From MaRDI portal
Publication:3031861
DOI10.1051/m2an/1987210405811zbMath0689.65065OpenAlexW2464997744MaRDI QIDQ3031861
Jim jun. Douglas, Franco Brezzi, Michel Fortin, Luisa Donatella Marini
Publication date: 1987
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/193515
mixed finite elementsrates of convergencesecond order elliptic equationsrectangular elementsRaviart-Thomas elementsalternating- direction iterative techniques
Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods, Multilevel iterative methods for mixed finite element discretizations of elliptic problems, Superconvergence ofH1-Galerkin Mixed Finite Element Methods for Second-Order Elliptic Equations, Domain decomposition and expanded mixed method for parabolic partial differential equations, Splitting positive definite mixed element methods for pseudo-hyperbolic equations, Conditions for superconvergence of HDG methods for second-order elliptic problems, Numerical solution of the acoustic wave equation using Raviart-Thomas elements, A rectangular mixed element method with continuous flux approximation for coupling Stokes and Darcy flows, Globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamic equations, A multiscale domain decomposition approach for parabolic equations using expanded mixed method, Block iterative solvers for higher order finite volume methods, A new locking-free equilibrium mixed element for plane elasticity with continuous displacement interpolation, Least-squares Galerkin procedures for pseudohyperbolic equations, Crank--Nicolson least-squares Galerkin procedures for parabolic integro-differential equations, Interior superconvergence in mortar and non-mortar mixed finite element methods on non-matching grids, Superconvergent pseudostress-velocity finite element methods for the Oseen equations, Continuous-time finite element analysis of multiphase flow in groundwater hydrology, Schwarz algorithms for the Raviart-Thomas mixed method, Uniformly convergent cubic nonconforming element for Darcy-Stokes problem, Expanded mixed finite element method for the two-dimensional Sobolev equation, On the coupling of boundary integral and mixed finite element methods, Two dimensional mixed finite element approximations for elliptic problems with enhanced accuracy for the potential and flux divergence, Some observations on mixed methods for fully nonlinear parabolic problems in divergence form, High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling, Guaranteed a posteriori error estimator for mixed finite element methods of elliptic problems, A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids, Mixed element method for two-dimensional Darcy-Forchheimer model, A stabilized mixed finite element method for steady and unsteady reaction-diffusion equations, Analytical and variational numerical methods for unstable miscible displacement flows in porous media, Third order nodal finite element methods with transverse and reduced integration for elliptic problems, A priori error estimates of multiblock mortar expanded mixed method for elliptic problems, A new combined characteristic mixed finite element method for compressible miscible displacement problem, Continuous mixed finite elements for the second order elliptic equation with a low order term, Hierarchical high order finite element spaces in \(H(\operatorname{div},\Omega)\times H^1(\Omega)\) for a stabilized mixed formulation of Darcy problem, Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations, Dual-scale Galerkin methods for Darcy flow, Mixed finite element methods for general quadrilateral grids, Dispersion analysis of the \(P_n - P_{n - 1}^{\mathrm{DG}}\) mixed finite element pair for atmospheric modelling, Expanded mixed finite element method for second order hyperbolic equations, A remark concerning divergence accuracy order for \(\mathbf H(\operatorname{div})\)-conforming finite element flux approximations, Uncoupling evolutionary groundwater-surface water flows: stabilized mixed methods in both porous media and fluid regions, Mixed methods with dynamic finite-element spaces for miscible displacement in porous media, A multiscale preconditioner for stochastic mortar mixed finite elements, Stabilized finite element method for the stationary mixed Stokes-Darcy problem, Some new families of finite elements for the Stokes equations, Prismatic mixed finite elements for second order elliptic problems, A simple preconditioner for a discontinuous Galerkin method for the Stokes problem, Mixed finite elements for numerical weather prediction, Composable block solvers for the four-field double porosity/permeability model, On the heterogeneous multiscale method with various macroscopic solvers, Superconvergence of least-squares mixed finite element for symmetric elliptic problems., A new MMOCAA-MFE method for compressible miscible displacement in porous media, A mixed element method for Darcy-Forchheimer incompressible miscible displacement problem, Globally constraint-preserving FR/DG scheme for Maxwell's equations at all orders, Some least-squares Galerkin procedures for first-order time-dependent convection-diffusion system, Implementation of a mortar mixed finite element method using a multiscale flux basis, A unified study of continuous and discontinuous Galerkin methods, Analysis of multiscale mortar mixed approximation of nonlinear elliptic equations, A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media, Numerical solutions of the incompressible miscible displacement equations in heterogeneous media, The splitting mixed element method for parabolic equation and its application in chemotaxis model, New curl conforming finite elements on parallelepiped, A weak Galerkin-mixed finite element method for the Stokes-Darcy problem, A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model, High-order composite finite element exact sequences based on tetrahedral-hexahedral-prismatic-pyramidal partitions, A characteristic mixed method with dynamic finite-element space for convection-dominated diffusion problems, Analysis of mixed finite element methods on locally refined grids, Splitting positive definite mixed element method for viscoelasticity wave equation, A new positive definite expanded mixed finite element method for parabolic integrodifferential equations, Superconvergence of new mixed finite element spaces, Characteristic splitting mixed finite element analysis of compressible wormhole propagation, A rectangular mixed finite element method with a continuous flux for an elliptic equation modelling Darcy flow, Superconvergence for rectangular mixed finite elements, The Lagrange multipliers in the equilibrium finite element method: Error estimates and postprocessing, Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems, A strongly conservative finite element method for the coupling of Stokes and Darcy flow, Stochastic collocation and mixed finite elements for flow in porous media, A splitting positive definite mixed finite element method for two classes of integro-differential equations, Multiscale mortar expanded mixed discretization of nonlinear elliptic problems, A splitting positive definite mixed finite element method for elliptic optimal control problem, Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction, Domain decomposition for coupled Stokes and Darcy flows, Multiscale mortar mixed domain decomposition approximations of nonlinear parabolic equations, Superconvergence of mixed finite element methods on rectangular domains, A characteristic mixed element method for displacement problems of compressible flow in porous media, Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth, An IMPES scheme for a two-phase flow in heterogeneous porous media using a structured grid, Three dimensional hierarchical mixed finite element approximations with enhanced primal variable accuracy, Generalized local projection stabilized nonconforming finite element methods for Darcy equations, Locking-free Reissner-Mindlin elements without reduced integration, Full-order convergence of a mixed finite element method for fourth-order elliptic equations, Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation, Multigrid on the interface for mortar mixed finite element methods for elliptic problems, Optimal \(H(\mathrm{div})\) flux approximations from the primal hybrid finite element method on quadrilateral meshes, A new family of expanded mixed finite element methods for reaction-diffusion equations, A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem, The discontinuous Petrov-Galerkin method for elliptic problems, Transparent boundary conditions for the shallow water equations with a mixed finite element formulation, Commuting diagrams for the TNT elements on cubes, A stabilized mixed finite element method for Darcy flow, Canonical construction of finite elements, Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems, Finite element method for the Stokes-Darcy problem with a new boundary condition, Hybrid Mixed Finite Element Formulations Based on a Least-Squares Approach, A numerical study of fluids with pressure-dependent viscosity flowing through a rigid porous medium, Mixed Finite Element Methods for Compressible Miscible Displacement in Porous Media, Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates, Analysis of the Schwarz algorithm for mixed finite elements methods, Hierarchic and mixed‐interpolated finite elements for Reissner–Mindlin problems, Transformations for Piola-mapped elements, Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids, Mathematical modeling of the multicomponent flow in porous media using higher-order methods, A posteriori error estimates for primal hybrid finite element methods applied to Poisson problem, A stabilized mixed finite element method for the first‐order form of advection–diffusion equation, Constraint-Satisfying Krylov Solvers for Structure-Preserving Discretizations, Superconvergence by $M$-decompositions. Part I: General theory for HDG methods for diffusion, Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations, Interior penalty preconditioners for mixed finite element approximations of elliptic problems, Domain decomposition algorithms for mixed methods for second-order elliptic problems, Unnamed Item, On a Second-Order Multipoint Flux Mixed Finite Element Methods on Hybrid Meshes, On the simulation of incompressible, miscible displacement in a naturally fractured petroleum reservoir, New Mixed Finite Volume Spaces for Elliptic Problems on Parallelepiped, Sharp maximum norm error estimates for general mixed finite element approximations to second order elliptic equations, DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM, Conditions for superconvergence of HDG methods for Stokes flow, Substructure Preconditioners for Elliptic Saddle Point Problems, Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry, Unnamed Item, Balancing Domain Decomposition for Mixed Finite Elements, The discontinuous enrichment method, Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems, Nonconforming elements in least-squares mixed finite element methods, Analysis of multilevel decomposition iterative methods for mixed finite element methods, A Dual–Mixed Finite Element Method for the Brinkman Problem, Stability and convergence of mixed discontinuous finite element methods for second-order differential problems, New mixed finite volume methods for second order eliptic problems, Unnamed Item, Black Box Multigrid with coarsening by a factor of three, Enforcing the non-negativity constraint and maximum principles for diffusion with decay on general computational grids, Expanded mixed finite element methods for linear second-order elliptic problems, I, Expanded mixed finite element methods for quasilinear second order elliptic problems, II, Convergence of a high order method in time and space for the miscible displacement equations, Unnamed Item, A New Family of Efficient Conforming Mixed Finite Elements on Both Rectangular and Cuboid Meshes for Linear Elasticity in the Symmetric Formulation
Cites Work
- Alternating direction methods for three space variables
- Two families of mixed finite elements for second order elliptic problems
- Mixed finite elements for second order elliptic problems in three variables
- The finite element method with Lagrangian multipliers
- Global Estimates for Mixed Methods for Second Order Elliptic Equations
- Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
- Higher Order Local Accuracy by Averaging in the Finite Element Method
- An analysis of the convergence of mixed finite element methods
- Interior and superconvergence estimates for mixed methods for second order elliptic problems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item