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Numerical Functional Analysis and Optimization Volume 26, 2005 - Issue 6
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Original Articles

Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra I: A Priori Estimates

Constantin Bacuta Mathematical Sciences, University of Delaware, Newark, Delaware, USACorrespondence[email protected]
,
Victor Nistor Mathematics Department, Pennsylvania State University, University Park, Pennsylvania, USA
&
Ludmil T. Zikatanov Mathematics Department, Pennsylvania State University, University Park, Pennsylvania, USA
Pages 613-639 | Received 05 May 2005, Accepted 07 Jul 2005, Published online: 16 Aug 2006

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Constantin Bacuta. (2008) Subspace Interpolation with Applications to Elliptic Regularity. Numerical Functional Analysis and Optimization 29:1-2, pages 88-114.
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Constantin Bacuta, Victor Nistor & LudmilT. Zikatanov. (2007) Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra II: Mesh Refinements and Interpolation. Numerical Functional Analysis and Optimization 28:7-8, pages 775-824.
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Articles from other publishers (39)

Ilaria Perugia, Christoph Schwab & Marco Zank. (2023) Exponential convergence of hp -time-stepping in space-time discretizations of parabolic PDES . ESAIM: Mathematical Modelling and Numerical Analysis 57:1, pages 29-67.
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Josef DickMarcello Longo & Christoph Schwab. (2022) Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification. SIAM/ASA Journal on Uncertainty Quantification 10:2, pages 651-686.
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Wen-Ming He & Hailong Guo. (2022) Optimal Maximum Norm Estimates for Virtual Element Methods. SIAM Journal on Numerical Analysis 60:3, pages 1251-1280.
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Mirela Kohr & Victor Nistor. (2022) Sobolev spaces and $$\nabla $$-differential operators on manifolds I: basic properties and weighted spaces. Annals of Global Analysis and Geometry 61:4, pages 721-758.
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Wen-ming He & Ren Zhao. (2021) Local ultraconvergence of quadratic element. Calcolo 58:3.
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Wen‐ming He, Ren Zhao & Yong Cao. (2021) Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions. Numerical Methods for Partial Differential Equations.
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Xiong Liu. (2021) Superconvergence of the High-Degree FE Method for Second-Degree Elliptic Problem with Periodic Boundary. Mediterranean Journal of Mathematics 18:3.
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Wenming He, Ren Zhao, Guanrong Li & Wulan Li. (2020) Local ultraconvergence of finite element methods for second‐order elliptic problems with singularity . Numerical Methods for Partial Differential Equations 37:3, pages 2132-2149.
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Wen-ming He, Ren Zhao, Guanrong Li, Jin Xiao & Wulan Li. (2020) The optimal convergence of finite element methods for the three-dimensional second-order elliptic boundary value problem with singularity. Journal of Mathematical Analysis and Applications 491:2, pages 124369.
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Wen-ming He, Runchang Lin & Zhimin Zhang. (2020) Local ultraconvergence of linear and bilinear finite element method for second order elliptic problems. Journal of Computational and Applied Mathematics 372, pages 112715.
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OLESYA GRISHCHENKO, XIAO HAN & VICTOR NISTOR. (2020) A VOLATILITY-OF-VOLATILITY EXPANSION OF THE OPTION PRICES IN THE SABR STOCHASTIC VOLATILITY MODEL. International Journal of Theoretical and Applied Finance 23:03, pages 2050018.
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Wen‐ming He. (2019) The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition. Numerical Methods for Partial Differential Equations 35:6, pages 2044-2055.
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Constantin Bacuta & Jacob Jacavage. (2019) A Non-conforming Saddle Point Least Squares Approach for an Elliptic Interface Problem. Computational Methods in Applied Mathematics 19:3, pages 399-414.
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Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens, Rob Scheichl & Ian H. Sloan. (2018) Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. Numerische Mathematik 140:2, pages 479-511.
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Hengguang Li. (2017) An anisotropic finite element method on polyhedral domains: Interpolation error analysis. Mathematics of Computation 87:312, pages 1567-1600.
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Wenming He, Zhimin Zhang & Qingsong Zou. (2017) Maximum-norms error estimates for high-order finite volume schemes over quadrilateral meshes. Numerische Mathematik.
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Wen-ming He, Zhimin Zhang & Qingsong Zou. (2016) Ultraconvergence of high order FEMs for elliptic problems with variable coefficients. Numerische Mathematik 136:1, pages 215-248.
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S. Ariche, C. De Coster & S. Nicaise. (2017) Regularity of solutions of elliptic problems with a curved fracture. Journal of Mathematical Analysis and Applications 447:2, pages 908-932.
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Roman Kvasov & Lev Steinberg. (2017) Modeling of Size Effects in Bending of Perforated Cosserat Plates. Modelling and Simulation in Engineering 2017, pages 1-19.
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Constantin Bacuta & Klajdi Qirko. (2017) A saddle point least squares approach for primal mixed formulations of second order PDEs. Computers & Mathematics with Applications 73:2, pages 173-186.
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Wen-ming He, Runchang Lin & Zhimin Zhang. (2016) Ultraconvergence of Finite Element Method by Richardson Extrapolation for Elliptic Problems with Constant Coefficients. SIAM Journal on Numerical Analysis 54:4, pages 2302-2322.
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Wenming He, Zhimin Zhang & Ren Zhao. (2015) The Highest Superconvergence of the Tri-linear Element for Schr $$\ddot{\text {o}}$$ o ¨ dinger Operator with Singularity. Journal of Scientific Computing 66:1, pages 1-18.
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Christoph Schwab. 2015. Encyclopedia of Applied and Computational Mathematics. Encyclopedia of Applied and Computational Mathematics 903 913 .
Hengguang Li & Jeffrey S. Ovall. (2014) A posteriori error estimation of hierarchical type for the Schrödinger operator with inverse square potential. Numerische Mathematik 128:4, pages 707-740.
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Eugénie Hunsicker, Hengguang Li, Victor Nistor & Ville Uski. (2014) Analysis of Schrödinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case. Numerical Methods for Partial Differential Equations 30:4, pages 1130-1151.
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Constantin Bacuta. (2014) Cascadic multilevel algorithms for symmetric saddle point systems. Computers & Mathematics with Applications 67:10, pages 1905-1913.
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Anna L. Mazzucato, Victor Nistor & Qingqin Qu. (2014) Quasi-optimal rates of convergence for the Generalized Finite Element Method in polygonal domains. Journal of Computational and Applied Mathematics 263, pages 466-477.
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H. Egger, U. Rüde & B. Wohlmuth. (2014) Energy-Corrected Finite Element Methods for Corner Singularities. SIAM Journal on Numerical Analysis 52:1, pages 171-193.
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Constantin Bacuta & Lu Shu. (2013) Multilevel Gradient Uzawa Algorithms for Symmetric Saddle Point Problems. Journal of Scientific Computing 57:1, pages 105-123.
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VICTOR NISTOR & CHRISTOPH SCHWAB. (2013) HIGH-ORDER GALERKIN APPROXIMATIONS FOR PARAMETRIC SECOND-ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS. Mathematical Models and Methods in Applied Sciences 23:09, pages 1729-1760.
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MARTIN COSTABEL, MONIQUE DAUGE & SERGE NICAISE. (2012) ANALYTIC REGULARITY FOR LINEAR ELLIPTIC SYSTEMS IN POLYGONS AND POLYHEDRA. Mathematical Models and Methods in Applied Sciences 22:08, pages 1250015.
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Constantin Bacuta & Peter Monk. (2012) Multilevel discretization of symmetric saddle point systems without the discrete LBB condition. Applied Numerical Mathematics 62:6, pages 667-681.
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Vu Trong Luong & Do Van Loi. (2011) Initial boundary value problems for second order parabolic systems in cylinders with polyhedral base. Boundary Value Problems 2011:1.
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Hengguang Li. (2011) Finite element analysis for the axisymmetric Laplace operator on polygonal domains. Journal of Computational and Applied Mathematics 235:17, pages 5155-5176.
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Constantin Bacuta, Brendan McCracken & Lu Shu. (2011) Residual reduction algorithms for nonsymmetric saddle point problems. Journal of Computational and Applied Mathematics 235:6, pages 1614-1628.
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Anna L. Mazzucato & Victor Nistor. (2008) Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks. Archive for Rational Mechanics and Analysis 195:1, pages 25-73.
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Hengguang Li & Victor Nistor. (2009) Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM. Journal of Computational and Applied Mathematics 224:1, pages 320-338.
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Z. Cai & C. R. Westphal. (2008) A Weighted $H(div)$ Least-Squares Method for Second-Order Elliptic Problems. SIAM Journal on Numerical Analysis 46:3, pages 1640-1651.
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Bernd Ammann & Victor Nistor. (2007) Weighted Sobolev spaces and regularity for polyhedral domains. Computer Methods in Applied Mechanics and Engineering 196:37-40, pages 3650-3659.
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