A new \(P_1\) weak Galerkin method for the biharmonic equation
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Publication:2279881
DOI10.1016/j.cam.2019.07.002zbMath1427.65342OpenAlexW2959514605MaRDI QIDQ2279881
Shangyou Zhang, Zhimin Zhang, Xiu Ye
Publication date: 16 December 2019
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2019.07.002
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Variational methods for elliptic systems (35J50) A priori estimates in context of PDEs (35B45) Variational methods for higher-order elliptic equations (35J35)
Related Items (11)
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem ⋮ A Mathematical Analysis Method for Bending Problem of Clamped Shallow Spherical Shell on Elastic Foundation ⋮ \(C^1\)-conforming variational discretization of the biharmonic wave equation ⋮ A family of H-div-div mixed triangular finite elements for the biharmonic equation ⋮ Four-order superconvergent weak Galerkin methods for the biharmonic equation on triangular meshes ⋮ Four-order superconvergent CDG finite elements for the biharmonic equation on triangular meshes ⋮ A Conforming Dg Method for the Biharmonic Equation on Polytopal Meshes ⋮ A stabilizer-free \(C^0\) weak Galerkin method for the biharmonic equations ⋮ A Stabilizer Free Weak Galerkin Method for the Biharmonic Equation on Polytopal Meshes ⋮ A new \(P_0\) weak Galerkin finite element scheme for second-order problems ⋮ On the uniform convergence of the weak Galerkin finite element method for a singularly-perturbed biharmonic equation
Cites Work
- A \(C^0\)-weak Galerkin finite element method for the biharmonic equation
- A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order
- \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
- Approximation of the biharmonic problem using piecewise linear finite elements
- Mixed discontinuous Galerkin finite element method for the biharmonic equation
- A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems
- \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
- A family of 3D continuously differentiable finite elements on tetrahedral grids
- A \(C^0\) linear finite element method for biharmonic problems
- Polynomial approximation on tetrahedrons in the finite element method
- 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
- An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes
- A conforming finite element for plate bending
- On the finite element method
- A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations
- A superconvergence of the Morley element via postprocessing
- Approximation of the biharmonic problem using P1 finite elements
- The Lowest Order Differentiable Finite Element on Rectangular Grids
- A weak Galerkin mixed finite element method for second order elliptic problems
- Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
- A Mixed Finite Element Method for the Biharmonic Equation
- A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
- On Cubic and Quartic Clough–Tocher Finite Elements
- Piecewise Quadratic Approximations on Triangles
- Approximation of the Biharmonic Equation by a Mixed Finite Element Method
- Minimal finite element spaces for $2m$-th-order partial differential equations in $R^n$
- On the Full C<sub>1</sub>-Q<sub>k</sub> Finite Element Spaces on Rectangles and Cuboids
- Development of a P2 element with optimal L2 convergence for biharmonic equation
- Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
- A C1-P2 finite element without nodal basis
- The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids
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