The local superconvergence of the quadratic triangular element for the poisson problem in a polygonal domain
DOI10.1002/num.21881zbMath1407.65261OpenAlexW1934203812MaRDI QIDQ4982258
Qiding Zhu, Wen-ming He, Jun-Zhi Cui
Publication date: 24 March 2015
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.21881
Poisson equationweak estimateslocal symmetric techniquelocal superconvergencepolygonal boundaryquadratic triangular elements
Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The ultraconvergence of derivative for bicubic finite element
- Superconvergence in high-order Galerkin finite element methods
- An acceleration method for integral equations by using interpolation post-processing
- Ultraconvergence of ZZ patch recovery at mesh symmetry points
- Superconvergence in Galerkin finite element methods
- Error estimates of finite element method about elliptic problems with singular righthand side
- A new superconvergence and extrapolation for second order triangular element
- Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part 1: A smooth problem and globally quasi-uniform meshes
- Asymptotic Error Expansions for the Finite Element Method for Second Order Elliptic Problems in $R^N$, $N\geq2$. I: Local Interior Expansions
- A new approach to Richardson extrapolation in the finite element method for second order elliptic problems
- A Priori Mesh Grading for an Elliptic Problem with Dirac Right-Hand Side
- Derivative superconvergent points in finite element solutions of harmonic functions--- A theoretical justification
- A numerical approximation to the solution of an inverse heat conduction problem
- Natural Superconvergence Points in Three-Dimensional Finite Elements
- The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
- Interpolated Boundary Conditions in the Finite Element Method
- Pointwise superconvergence of the gradient for the linear tetrahedral element
- Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates
- Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case
- Natural superconvergent points of triangular finite elements
- Superconvergence in Finite Element Methods and Meshes That are Locally Symmetric with Respect to a Point
- Superconvergence of interpolated collocation solutions for Hammerstein equations
- A New Finite Element Gradient Recovery Method: Superconvergence Property
- Pointwise supercloseness of tensor‐product block finite elements
- Weighted Sobolev Spaces and Degenerate Elliptic Equations
- The local superconvergence of the linear finite element method for the poisson problem
- Maximum‐norm superapproximation of the gradient for the trilinear block finite element
- ISOLATION OF SINGULARITIES OF THE GREEN'S FUNCTION
This page was built for publication: The local superconvergence of the quadratic triangular element for the poisson problem in a polygonal domain