On the Implementation of Mixed Methods as Nonconforming Methods for Second- Order Elliptic Problems

DOI10.2307/2153478zbMath0829.65127OpenAlexW2031182879MaRDI QIDQ4846162

Todd Arbogast, Zhang-Xin Chen

Publication date: 22 January 1996

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: http://purl.umn.edu/2492

zbMATH Keywords

Galerkin methodmixed finite element methodsvariable coefficientsmultigrid algorithmssecond-order elliptic problemnonconforming methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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

Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework, Stability of mixed FEMs for non-selfadjoint indefinite second-order linear elliptic PDEs, Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods, Guaranteed a posteriori error estimates for a staggered discontinuous Galerkin method, Uniform convergence and Schwarz method for the mortar projection nonconforming and mixed element methods for nonselfadjoint and indefinite problems, Locally conservative, stabilized finite element methods for variably saturated flow, Modeling and simulation of thermo-fluid-electrochemical ion flow in biological channels, Convergence of nonconforming $V$-cycle and $F$-cycle multigrid algorithms for second order elliptic boundary value problems, Comparison of various formulations of three-phase flow in porous media, Error analysis of variable degree mixed methods for elliptic problems via hybridization, Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations., Adaptive mesh refinement and multilevel iteration for flow in porous media, Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients, A multiscale thermo-fluid computational model for a two-phase cooling system, A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations, Equilibrated stress tensor reconstruction and a posteriori error estimation for nonlinear elasticity, Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes, Analysis of mortar-type \(Q_1^{\mathrm{rot}}/Q_0\) element and multigrid methods for the incompressible Stokes problem, Guaranteed a posteriori error estimator for mixed finite element methods of elliptic problems, A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations, A posteriori error estimates for mixed approximations of degenerate elliptic problems, A nonconforming immersed virtual element method for elliptic interface problems, The Discrete Raviart-Thomas Mixed Finite Element Method for the $P$-Laplace Equation, Robust and local optimal a priori error estimates for interface problems with low regularity: mixed finite element approximations, A type of multi-level correction scheme for eigenvalue problems by nonconforming finite element methods, Mixed and nonconforming finite element approximations of Reissner-Mindlin plates., Domain decomposition algorithms for mixed methods for second-order elliptic problems, A simple nonconforming quadrilateral finite element, On the heterogeneous multiscale method with various macroscopic solvers, From face to element unknowns by local static condensation with application to nonconforming finite elements, Uniformly convergent \(H(\mathrm{div})\)-conforming rectangular elements for Darcy-Stokes problem, Convergence and domain decomposition algorithm for nonconforming and mixed methods for nonselfadjoint and indefinite problems, Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems, A new class of nonconforming finite elements for the enrichment of \(Q_{1}\) element on convex polytope, An ELLAM-MFEM solution technique for compressible fluid flows in porous media with point sources and sinks, A general approach to the construction of nonconforming finite elements on convex polytopes, Performance Analysis of Block AMG Preconditioning of Poroelasticity Equations, Robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients on anisotropic meshes, Asymptotically exact a posteriori error analysis for the mixed Laplace eigenvalue problem, Nonconforming FEMs for the $p$-Laplace Problem, Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot's consolidation model, New Mixed Finite Volume Spaces for Elliptic Problems on Parallelepiped, A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations, Multigrid and multilevel methods for nonconforming 𝑄₁ elements, Multigrid Algorithms for Nonconforming and Mixed Methods for Nonsymmetric and Indefinite Problems, Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations, A unified framework for a posteriori error estimation for the Stokes problem, Nonconforming finite element approximation of crystalline microstructure, A conservative level set method suitable for variable-order approximations and unstructured meshes, Characteristic-nonconforming finite-element methods for advection-dominated diffusion problems, Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems, Nonconforming finite element approximations of the Steklov eigenvalue problem, Sharp algebraic and total a posteriori error bounds for \(h\) and \(p\) finite elements via a multilevel approach. Recovering mass balance in any situation, Superconvergent flux recovery of the Rannacher-Turek nonconforming element, Nonconforming discretizations of convex minimization problems and precise relations to mixed methods, Guaranteed and asymptotically exact a posteriori error estimator for lowest-order Raviart-Thomas mixed finite element method, Bubble stabilized discontinuous Galerkin method for parabolic and elliptic problems, Nonconforming elements in least-squares mixed finite element methods, BPX Preconditioner for Nonstandard Finite Element Methods for Diffusion Problems, Projection finite element methods for semiconductor device equations, A stabilized dual mixed hybrid finite element method with Lagrange multipliers for three-dimensional elliptic problems with internal interfaces, Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions, An additive Schwarz preconditioner for the mortar-type rotated \(Q_1\) FEM for elliptic problems with discontinuous coefficients, New mixed finite volume methods for second order eliptic problems, Error indicators for incompressible Darcy flow problems using enhanced velocity mixed finite element method, Algebraic Hybridization and Static Condensation with Application to Scalable $H$(div) Preconditioning, A low order anisotropic nonconforming characteristic finite element method for a convection-dominated transport problem, Uniform convergence and preconditioning methods for projection nonconforming and mixed methods for nonselfadjoint and indefinite problems, Expanded mixed finite element methods for linear second-order elliptic problems, I, Preconditioning projection nonconforming element method for the lowest-order Raviart-Thomas mixed triangular element method, \(\mathcal V\)-cycle Galerkin-multigrid methods for nonconforming methods for nonsymmetric and indefinite problems, Convergence of nonconforming multigrid methods without full elliptic regularity, Nonconforming FEMs for an Optimal Design Problem, Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations, Lower bounds of the discretization error for piecewise polynomials, Multigrid method and multilevel additive preconditioner for mixed element method for non-self-adjoint and indefinite problems, Additive Schwarz methods for the Crouzeix-Raviart mortar finite element for elliptic problems with discontinuous coefficients, A Parallel Preconditioner for a FETI-DP Method for the Crouzeix–Raviart Finite Element, A parallel domain decomposition algorithm of mixed element equation for second-order elliptic Dirichlet boundary value problem, The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements