A family of non-conforming elements and the analysis of Nitsche's method for a singularly perturbed fourth order problem
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Publication:714669
DOI10.1007/s10092-011-0047-8zbMath1253.65150OpenAlexW2164000452MaRDI QIDQ714669
Johnny Guzmán, Dmitriy Leykekhman, Michael Neilan
Publication date: 11 October 2012
Published in: Calcolo (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10092-011-0047-8
Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Singular perturbations of ordinary differential equations (34D15)
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Cites Work
- Unnamed Item
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- \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
- A new robust \(C^{0}\)-type nonconforming triangular element for singular perturbation problems
- Robustness of a spline element method with constraints
- On the role of boundary conditions for CIP stabilization of higher order finite elements
- Weak imposition of Dirichlet boundary conditions in fluid mechanics
- A discrete de Rham complex with enhanced smoothness
- \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
- Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow
- 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
- On some techniques for approximating boundary conditions in the finite element method
- Analysis of finite element methods for the Brinkman problem
- 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)
- A robust nonconforming $H^2$-element
- On the Necessity and Sufficiency of the Patch Test for Convergence of Nonconforming Finite Elements
- A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem
- On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
- Conforming Finite Element Approximations for a Fourth-Order Singular Perturbation Problem
- Finite Element Methods for Elliptic Equations Using Nonconforming Elements
- Locking in finite-element approximations to long thin extensible beams
- The Mathematical Theory of Finite Element Methods
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