A new mixed finite-element method for \(H^2\) elliptic problems

DOI10.1016/j.camwa.2022.10.024zbMath1504.65254arXiv2105.07289OpenAlexW4309783585MaRDI QIDQ2107207

Yanyan Li

Publication date: 1 December 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.07289

zbMATH Keywords

biharmonic equationmultigrid methodssaddle-point problemsmixed finite-element methods

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Preconditioners for iterative methods (65F08) Elliptic equations and elliptic systems (35Jxx)

Uses Software

• PETSc
• MUMPS
• Firedrake

Cites Work

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• A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• A decomposition result for biharmonic problems and the Hellan-Herrmann-Johnson method
• \(hp\)-version interior penalty DGFEMs for the biharmonic equation
• Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
• Elliptic problems in domains with piecewise smooth boundaries
• Mixed finite element methods - reduced and selective integration techniques: a unification of concepts
• On the constants in \(hp\)-finite element trace inverse inequalities.
• Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems
• Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
• Multigrid in H(div) and H(curl)
• Nitsche's method for linear Kirchhoff-Love shells: formulation, error analysis, and verification
• Two stabilized three-field formulations for the biharmonic problem
• A stable mixed element method for the biharmonic equation with first-order function spaces
• A nonconforming scheme for non-Fickian flow in porous media
• The Morley element for fourth order elliptic equations in any dimensions
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• C 0 Interior Penalty Galerkin Method for Biharmonic Eigenvalue Problems
• Preconditioning discretizations of systems of partial differential equations
• Local Fourier analysis for multigrid with overlapping smoothers applied to systems of PDEs
• A new three-field formulation of the biharmonic problem and its finite element discretization
• Nitsche’s method for general boundary conditions
• A Mixed Method for the Biharmonic Problem Based On a System of First-Order Equations
• Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements
• MIXED FINITE ELEMENT APPROXIMATION OF THE VECTOR LAPLACIAN WITH DIRICHLET BOUNDARY CONDITIONS
• A Quadratic $C^0$ Interior Penalty Method for Linear Fourth Order Boundary Value Problems with Boundary Conditions of the Cahn--Hilliard Type
• Firedrake
• Energy Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects
• Numerical solution of saddle point problems
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• From Functional Analysis to Iterative Methods
• Finite Element Methods for Navier-Stokes Equations
• A Mixed Finite Element Method for the Biharmonic Equation
• Analysis of Mixed Methods Using Mesh Dependent Norms
• Analysis of Some Mixed Finite Element Methods Related to Reduced Integration
• Mixed and Hybrid Finite Element Methods
• The Finite Element Method with Penalty
• Finite Element Methods for Elliptic Equations Using Nonconforming Elements
• Preconditioning in H(𝑑𝑖𝑣) and applications
• A Note on Preconditioning for Indefinite Linear Systems
• Solver Composition Across the PDE/Linear Algebra Barrier
• Mixed Finite Element Methods and Applications
• Code Generation for Generally Mapped Finite Elements
• Finite Elements II
• PCPATCH
• The divDiv-complex and applications to biharmonic equations
• Monolithic Multigrid Methods for Magnetohydrodynamics
• An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier--Stokes Equations at High Reynolds Number
• Stable splitting of polyharmonic operators by generalized Stokes systems
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Finite Elemente
• Preconditioning a mass‐conserving discontinuous Galerkin discretization of the Stokes equations
• The Mathematical Theory of Finite Element Methods
• Multigrid Algorithms for C0 Interior Penalty Methods
• Nonconforming Elements in the Finite Element Method with Penalty
• Some mixed finite element methods for biharmonic equation

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