v0.14.0
Loading...
Searching...
No Matches
Bibliography
[1]

Mark Ainsworth and Joe Coyle. Hierarchic finite element bases on unstructured tetrahedral meshes. International Journal for Numerical Methods in Engineering, 58(14):2103–2130, 2003.

[2]

Mark Ainsworth and Guosheng Fu. Bernstein-bézier bases for tetrahedral finite elements. Computer Methods in Applied Mechanics and Engineering, 2018.

[3]

Mark Ainsworth, Gaelle Andriamaro, and Oleg Davydov. Bernstein-bézier finite elements of arbitrary order and optimal assembly procedures. SIAM Journal on Scientific Computing, 33(6):3087–3109, 2011.

[4]

Mark Ainsworth. Essential boundary conditions and multi-point constraints in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 190(48):6323–6339, 2001.

[5]

Mark Ainsworth. A posteriori error estimation for lowest order raviart-thomas mixed finite elements. SIAM Journal on Scientific Computing, 30(1):189–204, 2007.

[6]

Douglas N Arnold, Richard S Falk, and Ragnar Winther. Differential complexes and stability of finite element methods i. the de rham complex. In Compatible spatial discretizations, pages 23–46. Springer, 2006.

[7]

Douglas N Arnold, Richard S Falk, and Jay Gopalakrishnan. Mixed finite element approximation of the vector laplacian with dirichlet boundary conditions. Mathematical Models and Methods in Applied Sciences, 22(09):1250024, 2012.

[8]

Francesca Baldini, Alice Bartolozzi, Martina Ardito, Adriana Voci, Piero Portincasa, Massimo Vassalli, and Laura Vergani. Biomechanics of cultured hepatic cells during different steatogenic hits. Journal of the Mechanical Behavior of Biomedical Materials, 97:296–305, 2019.

[9]

Roshdy S Barsoum. On the use of isoparametric finite elements in linear fracture mechanics. International journal for numerical methods in engineering, 10(1):25–37, 1976.

[10]

William L Barth and Graham F Carey. On a boundary condition for pressure-driven laminar flow of incompressible fluids. International journal for numerical methods in fluids, 54(11):1313–1325, 2007.

[11]

Hadrien Bériot, Albert Prinn, and Gwénaël Gabard. Efficient implementation of high-order finite elements for helmholtz problems. International Journal for Numerical Methods in Engineering, 2015.

[12]

Daniele Boffi, Franco Brezzi, Michel Fortin, and others. Mixed finite element methods and applications, volume 44. Springer, 2013.

[13]

Dietrich Braess and Rüdiger Verfürth. A posteriori error estimators for the raviart-thomas element. SIAM Journal on Numerical Analysis, 33(6):2431–2444, 1996.

[14]

F Brezzi, D Boffi, L Demkowicz, RG Durán, RS Falk, and M Fortin. Mixed finite elements, compatibility conditions, and applications. Springer, 2008.

[15]

Carsten Carstensen. A posteriori error estimate for the mixed finite element method. Mathematics of Computation of the American Mathematical Society, 66(218):465–476, 1997.

[16]

Bernardo Cockburn, Jayadeep Gopalakrishnan, and Johnny Guzmán. A new elasticity element made for enforcing weak stress symmetry. Mathematics of Computation, 79(271):1331–1349, 2010.

[17]

B. Cotterell and J.R. Rice. Slightly curved or kinked cracks. International Journal of Fracture, 16(2):155–169, 1980.

[18]

Michael A Crisfield. A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements. Computer methods in applied mechanics and engineering, 81(2):131–150, 1990.

[19]

Eduardo A de Souza Neto, Djordje Peric, and David Roger Jones Owen. Computational methods for plasticity: theory and applications. John Wiley & Sons, 2011.

[20]

Leszek Demkowicz and Jayadeep Gopalakrishnan. Analysis of the dpg method for the poisson equation. SIAM Journal on Numerical Analysis, 49(5):1788–1809, 2011.

[21]

L. Demkowicz. Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1 One and Two Dimensional Elliptic and Maxwell Problems. Chapman & Hall/CRC Applied Mathematics & Nonlinear Science. CRC Press, 2006.

[22]

J Eitelberger, TK Bader, K De Borst, and A Jäger. Multiscale prediction of viscoelastic properties of softwood under constant climatic conditions. Computational Materials Science, 55:303–312, 2012.

[23]

Ronald Aylmer Fisher. The wave of advance of advantageous genes. Annals of eugenics, 7(4):355–369, 1937.

[24]

Yves Renard Franz Chouly, Patrick Hild. Symmetric and non-symmetric variants of nitsche’s method for contact problems in elasticity: theory and numerical experiments. Technical Report hal- 00776619, HAL archives-ovuertes.fr, 2013.

[25]

Federico Fuentes, Brendan Keith, Leszek Demkowicz, and Sriram Nagaraj. Orientation embedded high order shape functions for the exact sequence elements of all shapes. Computers & Mathematics with Applications, 70(4):353 – 458, 2015.

[26]

Federico Fuentes, Brendan Keith, Leszek Demkowicz, and Sriram Nagaraj. Orientation embedded high order shape functions for the exact sequence elements of all shapes. Computers & Mathematics with applications, 70(4):353–458, 2015.

[27]

R Hauptmann and K Schweizerhof. A systematic development of solid shell element formulations for linear and non linear analyses employing only displacement degrees of freedom. International Journal for Numerical Methods in Engineering, 42(1):49–69, 1998.

[28]

Yuhang Hu and Zhigang Suo. Viscoelasticity and poroelasticity in elastomeric gels. Acta Mechanica Solida Sinica, 25(5):441–458, 2012.

[29]

John W Hutchinson and Zhigang Suo. Mixed mode cracking in layered materials. Advances in applied mechanics, 29(63):191, 1992.

[30]

Olha Ivanyshyn, Erion Gjonaj, and Thomas Weiland. Computation of singular electromagnetic fields using a hybrid dg-fem method. In Electromagnetic Theory (EMTS), Proceedings of 2013 URSI International Symposium on, pages 745–748. IEEE, 2013.

[31]

Mika Juntunen and Rolf Stenberg. Nitsche’s method for general boundary conditions. Mathematics of computation, 78(267):1353–1374, 2009.

[32]

Łukasz Kaczmarczyk, Chris J. Pearce, and Nenad Bićanić. Scale transition and enforcement of rve boundary conditions in second-order computational homogenization. International Journal for Numerical Methods in Engineering, 74(3):506–522, 2008.

[33]

Lukasz Kaczmarczyk, Mohaddeseh Mousavi Nezhad, and Chris Pearce. Three-dimensional brittle fracture: configurational-force-driven crack propagation. International Journal for Numerical Methods in Engineering, 97(7):531–550, 2014.

[34]

Matthew G Knepley. Programming languages for scientific computing. arXiv preprint arXiv:1209.1711, 2012.

[35]

Walter Landry. Implementing a high performance tensor library. Scientific Programming, 11(4):273–290, 2003.

[36]

Aleksander Lovric, Wulf G Dettmer, and Djordje Peric. Low order finite element methods for the Navier-Stokes-Cahn-Hilliard equations. November 2019.

[37]

Kaczmarczyk Lukasz, Ullah Zahur, Lewandowski Karol, Meng Xuan, Zhou Xiao-Yi, Athanasiadis Ignatios, Nguyen Hoang, Chalons-Mouriesse Christophe-Alexandre, Richardson Euan, Miur Euan, Shvarts Andrei, Wakeni Mebratu, and Pearce Chris. MoFEM: an open source, parallel finite element library. The Journal of Open Source Software, 2020. http://mofem.eng.gla.ac.uk.

[38]

Christian Miehe and Matthias Lambrecht. Algorithms for computation of stresses and elasticity moduli in terms of seth–hill's family of generalized strain tensors. Communications in numerical methods in engineering, 17(5):337–353, 2001.

[39]

A Parvizi, J Müller, SA Funken, and CT Koch. A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation. Ultramicroscopy, 154:1–6, 2015.

[40]

Florin Radu, Iuliu Sorin Pop, and Peter Knabner. Order of convergence estimates for an euler implicit, mixed finite element discretization of richards' equation. SIAM Journal on Numerical Analysis, 42(4):1452–1478, 2004.

[41]

B Dayanand Reddy. Introductory functional analysis: with applications to boundary value problems and finite elements, volume 27. Springer Science & Business Media, 2013.

[42]

Sergey I Repin. A posteriori estimates for partial differential equations, volume 4. Walter de Gruyter, 2008.

[43]

Detlef Ruprecht and Heinrich Müller. A scheme for edge-based adaptive tetrahedron subdivision. Springer, 1998.

[44]

RK Scott, LM Harris, and LM Polvani. A test case for the inviscid shallow-water equations on the sphere. Quarterly Journal of the Royal Meteorological Society, 142(694):488–495, 2016.

[45]

Juan C Simo and Thomas JR Hughes. Computational inelasticity, volume 7. Springer Science & Business Media, 2006.

[46]

Jordi Capdevila Sola. Individual project 4: Linear structural analysis of an arch dam using the finite element method. Technical report, University of Glasgow, 2017. Report.

[47]

Theodore Sussman and Klaus Jurgen Bathe. 3d-shell elements for structures in large strains. Computers and Structures, 122:2 – 12, 2013. Computational Fluid and Solid Mechanics 2013Proceedings Seventh {MIT} Conference on Computational Fluid and Solid Mechanics.

[48]

Timothy J Tautges. Canonical numbering systems for finite-element codes. International Journal for Numerical Methods in Biomedical Engineering, 26(12):1559–1572, 2010.

[49]

M. Fulland V. Lazarus, F.-G. Buchholz and J. Wiebesiek. Comparison of predictions by mode ii or mode iii criteria on crack front twisting in three or four point bending experiments. International Journal of Fracture, 153:141–151, 2008.

[50]

T Vogel, M Th Van Genuchten, and M Cislerova. Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions. Advances in Water Resources, 24(2):133–144, 2000.

[51]

JS Vrentas, CM Jarzebski, and JL Duda. A deborah number for diffusion in polymer-solvent systems. AIChE Journal, 21(5):894–901, 1975.

[52]

Tobias Waffenschmidt, Andreas Menzel, and Ellen Kuhl. Anisotropic density growth of bone—a computational micro-sphere approach. International Journal of Solids and Structures, 49(14):1928–1946, 2012.

[53]

Christian Wieners. Taylor-hood elements in 3d. In Analysis and Simulation of Multifield Problems, pages 189–196. Springer, 2003.

[54]

Olgierd Cecil Zienkiewicz, Robert Leroy Taylor, Perumal Nithiarasu, and JZ Zhu. The finite element method, volume 3. McGraw-hill London, 1977.