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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 9
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Articles

The divDiv-complex and applications to biharmonic equations

Dirk Paulya Fakultät für Mathematik, Universität Duisburg-Essen, Essen, GermanyCorrespondence[email protected]
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Walter Zulehnerb Institut für Numerische Mathematik, Johannes Kepler Universität Linz, Linz, AustriaView further author information
Pages 1579-1630 | Received 19 Jun 2017, Accepted 26 Oct 2018, Published online: 30 Nov 2018

Citations (29)

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Dirk Pauly & Walter Zulehner. (2023) The elasticity complex: compact embeddings and regular decompositions. Applicable Analysis 102:16, pages 4393-4421.
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Articles from other publishers (28)

Adam Sky & Ingo Muench. (2024) Polytopal templates for semi-continuous vectorial finite elements of arbitrary order on triangulations and tetrahedralizations. Finite Elements in Analysis and Design 236, pages 104155.
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Jun Hu, Yizhou Liang & Ting Lin. (2024) Finite Element Grad Grad Complexes and Elasticity Complexes on Cuboid Meshes. Journal of Scientific Computing 99:2.
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Francesca Bonizzoni, Kaibo Hu, Guido Kanschat & Duygu Sap. (2024) Discrete tensor product BGG sequences: Splines and finite elements. Mathematics of Computation.
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Dirk Pauly & Michael Schomburg. (2023) Hilbert complexes with mixed boundary conditions part 3: Biharmonic complexes. Mathematical Methods in the Applied Sciences 47:6, pages 3847-3892.
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Long Chen & Xuehai Huang. (2024) A new div-div-conforming symmetric tensor finite element space with applications to the biharmonic equation. Mathematics of Computation.
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Adam Sky, Michael Neunteufel, Peter Lewintan, Andreas Zilian & Patrizio Neff. (2024) Novel -conforming finite elements for the relaxed micromorphic sequence . Computer Methods in Applied Mechanics and Engineering 418, pages 116494.
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Adam Sky, Michael Neunteufel, Jack S. Hale & Andreas Zilian. (2023) A Reissner–Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations. Computer Methods in Applied Mechanics and Engineering 416, pages 116291.
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Dirk Pauly & Nathanael Skrepek. (2022) A compactness result for the div-curl system with inhomogeneous mixed boundary conditions for bounded Lipschitz domains and some applications. ANNALI DELL'UNIVERSITA' DI FERRARA 69:2, pages 505-519.
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Francis R. A. Aznaran, Patrick E. Farrell & Robert C. Kirby. (2023) Transformations for Piola-mapped elements. The SMAI Journal of computational mathematics 8, pages 399-437.
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Andreas Čap & Kaibo Hu. (2023) BGG Sequences with Weak Regularity and Applications. Foundations of Computational Mathematics.
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Ralf Hiptmair, Dirk Pauly & Erick Schulz. (2023) Traces for Hilbert complexes. Journal of Functional Analysis 284:10, pages 109905.
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Michele Botti, Daniele A. Di Pietro & Marwa Salah. (2023) A serendipity fully discrete div-div complex on polygonal meshes. Comptes Rendus. Mécanique 351:S1, pages 1-31.
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Andrea Brugnoli, Ghislain Haine & Denis Matignon. (2023) Stokes-Dirac structures for distributed parameter port-Hamiltonian systems: An analytical viewpoint. Communications in Analysis and Mechanics 15:3, pages 362-387.
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Daniele Di Pietro & Jérôme Droniou. (2022) A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem. Mathematics of Computation 92:339, pages 51-77.
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Patrick E. Farrell, Abdalaziz Hamdan & Scott P. MacLachlan. (2022) A new mixed finite-element method for H2 elliptic problems. Computers & Mathematics with Applications 128, pages 300-319.
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Dirk Pauly & Michael Schomburg. (2022) Hilbert complexes with mixed boundary conditions—Part 2: Elasticity complex. Mathematical Methods in the Applied Sciences 45:16, pages 8971-9005.
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Pascal Weinmüller & Thomas Takacs. (2022) An approximate multi-patch space for isogeometric analysis with a comparison to Nitsche’s method . Computer Methods in Applied Mechanics and Engineering 401, pages 115592.
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Adam Sky, Ingo Muench & Patrizio Neff. (2022) On $$[H^{1}]^{3 \times 3}$$, $$[H(\text {curl})]^3$$ and $$H(\text {sym Curl})$$ finite elements for matrix-valued Curl problems. Journal of Engineering Mathematics 136:1.
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Xiu Ye & Shangyou Zhang. (2022) A family of H-div-div mixed triangular finite elements for the biharmonic equation. Results in Applied Mathematics 15, pages 100318.
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Jun Hu, Yizhou Liang & Rui Ma. (2022) Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System. SIAM Journal on Numerical Analysis 60:3, pages 1307-1330.
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Dirk Pauly & Marcus Waurick. (2022) The index of some mixed order Dirac type operators and generalised Dirichlet–Neumann tensor fields. Mathematische Zeitschrift 301:2, pages 1739-1819.
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Dirk Pauly & Michael Schomburg. (2022) Hilbert complexes with mixed boundary conditions part 1: de Rham complex. Mathematical Methods in the Applied Sciences 45:5, pages 2465-2507.
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Long Chen & Xuehai Huang. 2022. The Virtual Element Method and its Applications. The Virtual Element Method and its Applications 93 135 .
Long Chen & Xuehai Huang. (2021) Finite elements for divdiv conforming symmetric tensors in three dimensions. Mathematics of Computation.
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Douglas N. Arnold & Kaibo Hu. (2021) Complexes from Complexes. Foundations of Computational Mathematics 21:6, pages 1739-1774.
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Robert Beig & Piotr T Chruściel. (2020) On linearised vacuum constraint equations on Einstein manifolds*. Classical and Quantum Gravity 37:21, pages 215012.
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Dirk Pauly & Jan Valdman. (2020) Poincaré–Friedrichs type constants for operators involving grad, curl, and div: Theory and numerical experiments. Computers & Mathematics with Applications 79:11, pages 3027-3067.
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Marcus Waurick. (2019) Homogenisation and the weak operator topology. Quantum Studies: Mathematics and Foundations 6:3, pages 375-396.
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