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Numerical Functional Analysis and Optimization Volume 25, 2004 - Issue 5-6
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Original Articles

Poincaré–Friedrichs Inequalities for Piecewise H2 Functions

Susanne C. Brenner Department of Mathematics, University of South Carolina, Columbia, South Carolina, USA; Department of Mathematics, University of South Carolina, LeConte College, 1523 Greene St., Columbia, SC, 29208, USACorrespondence[email protected]
,
Kening Wang Department of Mathematics, University of South Carolina, Columbia, South Carolina, USA
&
Jie Zhao Department of Mathematics, University of South Carolina, Columbia, South Carolina, USA
Pages 463-478 | Published online: 31 Aug 2006

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Sudipto Chowdhury, Thirupathi Gudi & A.K. Nandakumaran. (2015) A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to C 0 IP Methods. Numerical Functional Analysis and Optimization 36:11, pages 1388-1419.
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Articles from other publishers (54)

Jiali Qiu, Fei Wang, Min Ling & Jikun Zhao. (2023) The interior penalty virtual element method for the fourth-order elliptic hemivariational inequality. Communications in Nonlinear Science and Numerical Simulation 127, pages 107547.
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Susanne C. Brenner, Li-yeng Sung & Zhiyu Tan. (2023) A finite element method for a two-dimensional Pucci equation. Comptes Rendus. Mécanique 351:S1, pages 1-16.
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Carsten CarstensenRekha KhotAmiya K. Pani. (2023) Nonconforming Virtual Elements for the Biharmonic Equation with Morley Degrees of Freedom on Polygonal Meshes. SIAM Journal on Numerical Analysis 61:5, pages 2460-2484.
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Z. Dong & L. Mascotto. (2023) $$hp$$-Optimal Interior Penalty Discontinuous Galerkin Methods for the Biharmonic Problem. Journal of Scientific Computing 96:1.
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Xuehai Huang & Feng Wang. (2023) Analysis of divergence free conforming virtual elements for the Brinkman problem. Mathematical Models and Methods in Applied Sciences 33:06, pages 1245-1280.
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Fang Feng & Jianguo Huang. (2023) The virtual element method for a nonhomogeneous double obstacle problem of Kirchhoff plate. Nonlinear Analysis: Real World Applications 71, pages 103831.
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Amanda E. Diegel & Natasha S. Sharma. (2022) A C 0 interior penalty method for the phase field crystal equation . Numerical Methods for Partial Differential Equations 39:3, pages 2510-2537.
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Jingmin Xia & Patrick E. Farrell. (2023) Variational and numerical analysis of a Q -tensor model for smectic-A liquid crystals . ESAIM: Mathematical Modelling and Numerical Analysis 57:2, pages 693-716.
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Jikun Zhao, Shipeng Mao, Bei Zhang & Fei Wang. (2023) The interior penalty virtual element method for the biharmonic problem. Mathematics of Computation.
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Chunyu ChenXuehai Huang & Huayi Wei. (2022) \({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension. SIAM Journal on Numerical Analysis 60:6, pages 3099-3123.
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Jiali Qiu, Jikun Zhao & Fei Wang. (2022) Nonconforming virtual element methods for the fourth-order variational inequalities of the first kind. Journal of Computational and Applied Mathematics, pages 115025.
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Shangyou Zhang. (2022) A subspace of linear nonconforming finite element for nearly incompressible elasticity and stokes flow. Journal of Numerical Mathematics 0:0.
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Andreas Dedner & Alice Hodson. (2022) Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients. IMA Journal of Numerical Analysis 42:2, pages 1364-1399.
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Fang Feng, Weimin Han & Jianguo Huang. (2022) A Nonconforming Virtual Element Method for a Fourth-order Hemivariational Inequality in Kirchhoff Plate Problem. Journal of Scientific Computing 90:3.
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Susanne C. Brenner, Li‐Yeng Sung & Kening Wang. (2021) Additive Schwarz preconditioners for C 0 interior penalty methods for the obstacle problem of clamped Kirchhoff plates . Numerical Methods for Partial Differential Equations 38:1, pages 102-117.
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Fang Feng, Weimin Han & Jianguo Huang. (2021) The virtual element method for an obstacle problem of a Kirchhoff-Love plate. Communications in Nonlinear Science and Numerical Simulation 103, pages 106008.
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Kamana Porwal & Pratibha Shakya. (2021) A finite element method for an elliptic optimal control problem with integral state constraints. Applied Numerical Mathematics 169, pages 273-288.
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Susanne C. Brenner, Li-yeng Sung, Zhiyu Tan & Hongchao Zhang. (2021) A convexity enforcing $${C}^{{0}}$$ interior penalty method for the Monge–Ampère equation on convex polygonal domains. Numerische Mathematik 148:3, pages 497-524.
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Susanne C. Brenner & Ellya L. Kawecki. (2021) Adaptive interior penalty methods for Hamilton–Jacobi–Bellman equations with Cordes coefficients . Journal of Computational and Applied Mathematics 388, pages 113241.
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Fei Wang & Jikun Zhao. (2021) Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem. IMA Journal of Numerical Analysis 41:2, pages 1496-1521.
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Jianguo Huang & Yue Yu. (2021) A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations. Journal of Computational and Applied Mathematics 386, pages 113229.
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Amanda E. Diegel. (2021) A C0 interior penalty method for the Cahn-Hilliard equation. Electronic Research Archive 0:0, pages 0.
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Andrea Bonito, Ricardo H. Nochetto & Dimitrios Ntogkas. (2021) DG approach to large bending plate deformations with isometry constraint. Mathematical Models and Methods in Applied Sciences 31:01, pages 133-175.
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Andrea Bonito, Ricardo H. Nochetto & Dimitris Ntogkas. (2020) Discontinuous Galerkin approach to large bending deformation of a bilayer plate with isometry constraint. Journal of Computational Physics 423, pages 109785.
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Susanne C. Brenner, Li-yeng Sung & Zhiyu Tan. (2020) A cubic interior penalty method for elliptic distributed optimal control problems with pointwise state and control constraints . Results in Applied Mathematics 7, pages 100119.
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Shuo Zhang. (2020) Minimal consistent finite element space for the biharmonic equation on quadrilateral grids. IMA Journal of Numerical Analysis 40:2, pages 1390-1406.
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Susanne C. Brenner. 2020. Advances in Mathematical Sciences. Advances in Mathematical Sciences 3 16 .
Chandi Bhandari, Ronald H.W. Hoppe & Rahul Kumar. (2019) A C 0 interior penalty discontinuous Galerkin Method for fourth‐order total variation flow. II: Existence and uniqueness . Numerical Methods for Partial Differential Equations 35:4, pages 1477-1496.
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Ronald H. W. Hoppe & Christopher Linsenmann. 2019. Contributions to Partial Differential Equations and Applications. Contributions to Partial Differential Equations and Applications 297 325 .
Hao Li & Yidu Yang. (2018) An adaptive C0IPG method for the Helmholtz transmission eigenvalue problem. Science China Mathematics 61:8, pages 1519-1542.
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Long Chen, Jun Hu & Xuehai Huang. (2017) Fast auxiliary space preconditioners for linear elasticity in mixed form. Mathematics of Computation 87:312, pages 1601-1633.
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Jikun Zhao, Bei Zhang, Shaochun Chen & Shipeng Mao. (2017) The Morley-Type Virtual Element for Plate Bending Problems. Journal of Scientific Computing 76:1, pages 610-629.
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Hao Li & Yidu Yang. (2017) C 0IPG adaptive algorithms for the biharmonic eigenvalue problem. Numerical Algorithms 78:2, pages 553-567.
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P. F. Antonietti, G. Manzini & M. Verani. (2017) The fully nonconforming virtual element method for biharmonic problems. Mathematical Models and Methods in Applied Sciences 28:02, pages 387-407.
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Susanne C. Brenner, Joscha Gedicke & Li-yeng Sung. (2018) $C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State Constraints. SIAM Journal on Numerical Analysis 56:3, pages 1758-1785.
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Susanne C. Brenner, Thirupathi Gudi, Kamana Porwal & Li-yeng Sung. (2018) A morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints. ESAIM: Control, Optimisation and Calculus of Variations 24:3, pages 1181-1206.
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Susanne C. Brenner & Carsten Carstensen. 2018. Encyclopedia of Computational Mechanics Second Edition. Encyclopedia of Computational Mechanics Second Edition 1 47 .
Sudipto Chowdhury & Thirupathi Gudi. (2017) A interior penalty method for the Dirichlet control problem governed by biharmonic operator . Journal of Computational and Applied Mathematics 317, pages 290-306.
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Susanne C. Brenner, Michael Neilan, Armin Reiser & Li-Yeng Sung. (2016) A $$C^0$$ C 0 interior penalty method for a von Kármán plate. Numerische Mathematik 135:3, pages 803-832.
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Susanne C. Brenner & Li-yeng Sung. (2017) A New Convergence Analysis of Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints. SIAM Journal on Control and Optimization 55:4, pages 2289-2304.
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Jiguang Sun & Aihui Zhou. 2016. Finite Element Methods for Eigenvalue Problems. Finite Element Methods for Eigenvalue Problems 173 208 .
Jikun Zhao, Shaochun Chen & Bei Zhang. (2016) The nonconforming virtual element method for plate bending problems. Mathematical Models and Methods in Applied Sciences 26:09, pages 1671-1687.
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Erik Burman. 2016. Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 93 127 .
Susanne C. Brenner. (2015) Forty Years of the Crouzeix-Raviart element. Numerical Methods for Partial Differential Equations 31:2, pages 367-396.
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Susanne C. Brenner, Peter Monk & Jiguang Sun. 2015. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 3 15 .
Thirupathi Gudi, Neela Nataraj & Kamana Porwal. (2014) An interior penalty method for distributed optimal control problems governed by the biharmonic operator. Computers & Mathematics with Applications 68:12, pages 2205-2221.
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R. Z. Dautov & E. M. Fedotov. (2014) Abstract theory of hybridizable discontinuous Galerkin methods for second-order quasilinear elliptic problems. Computational Mathematics and Mathematical Physics 54:3, pages 474-490.
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Guido Kanschat & Natasha Sharma. (2014) Divergence-Conforming Discontinuous Galerkin Methods and $C^0$ Interior Penalty Methods. SIAM Journal on Numerical Analysis 52:4, pages 1822-1842.
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S. C. Brenner, L.-Y. Sung & Y. Zhang. 2014. Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations. Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations 97 132 .
Susanne C. Brenner, Michael Neilan & Li-Yeng Sung. (2012) Isoparametric C 0 interior penalty methods for plate bending problems on smooth domains. Calcolo 50:1, pages 35-67.
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Anna L. Mazzucato, Victor Nistor & Qingqin Qu. (2013) A Nonconforming Generalized Finite Element Method for Transmission Problems. SIAM Journal on Numerical Analysis 51:1, pages 555-576.
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Susanne C. Brenner. 2012. Frontiers in Numerical Analysis - Durham 2010. Frontiers in Numerical Analysis - Durham 2010 79 147 .
Thirupathi Gudi. (2010) A new error analysis for discontinuous finite element methods for linear elliptic problems. Mathematics of Computation 79:272, pages 2169-2189.
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Shuang Li & Kening Wang. 2007. Domain Decomposition Methods in Science and Engineering XVI. Domain Decomposition Methods in Science and Engineering XVI 675 682 .

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