Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem
DOI10.1137/21M1408555zbMath1501.65111arXiv2103.16404OpenAlexW3142231631MaRDI QIDQ5043626
Publication date: 6 October 2022
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.16404
stabilityerror analysisbiharmonic problemweak Galerkin methodcomputational performancehybrid high-order methodfourth-order PDEs
Plates (74K20) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)
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Cites Work
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- \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
- Virtual element methods for plate bending problems
- A \(C^0\)-weak Galerkin finite element method for the biharmonic equation
- An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
- A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order
- Virtual element method for fourth order problems: \(L^2\)-estimates
- \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
- Mathematical aspects of discontinuous Galerkin methods.
- \(hp\)-version interior penalty DGFEMs for the biharmonic equation
- Hybrid high-order methods for finite deformations of hyperelastic materials
- The Morley-type virtual element for plate bending problems
- A hybrid high-order locking-free method for linear elasticity on general meshes
- Discontinuous skeletal gradient discretisation methods on polytopal meshes
- A hybrid high-order method for the steady incompressible Navier-Stokes problem
- 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
- A hybrid high-order method for incremental associative plasticity with small deformations
- A new \(P_1\) weak Galerkin method for the biharmonic equation
- High order exactly divergence-free Hybrid Discontinuous Galerkin methods for unsteady incompressible flows
- A weak Galerkin finite element method with polynomial reduction
- The Morley element for fourth order elliptic equations in any dimensions
- AC0-weak Galerkin finite element method for fourth-order elliptic problems
- Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods
- The nonconforming virtual element method for plate bending problems
- Static Condensation, Hybridization, and the Devising of the HDG Methods
- Superconvergence by $M$-decompositions. Part I: General theory for HDG methods for diffusion
- Finite Element Methods for Navier-Stokes Equations
- A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
- An Unfitted Hybrid High-Order Method for Elliptic Interface Problems
- The fully nonconforming virtual element method for biharmonic problems
- Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. II---Overconsistency and Classical Nonconforming Elements
- Spectral approximation of elliptic operators by the Hybrid High-Order method
- Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. III---Discontinuous Galerkin and Other Interior Penalty Methods
- Error estimates for some quasi-interpolation operators
- A Hybrid High-Order method for Kirchhoff–Love plate bending problems
- Finite Elements II
- Finite Elements I
- Lowest-order equivalent nonstandard finite element methods for biharmonic plates
- Hybrid high-order method for singularly perturbed fourth-order problems on curved domains
- A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics
- A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity
- Discontinuous Galerkin methods for the biharmonic problem
- Finite element quasi-interpolation and best approximation
- Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
- A quasi-optimal variant of the hybrid high-order method for elliptic partial differential equations with H−1 loads
- An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems
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