Nonconforming finite-element discretization of convex variational problems
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[1] F. Smithies. Linear Operators , 2019, Nature.
[2] M. Foss,et al. The Lavrentiev Gap Phenomenon in Nonlinear Elasticity , 2003 .
[3] J. Ball,et al. Discontinuous equilibrium solutions and cavitation in nonlinear elasticity , 1982, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.
[4] Zhiping Li. ELEMENT REMOVAL METHOD FOR SINGULAR MINIMIZERS IN PROBLEMS OF HYPERELASTICITY , 1995 .
[5] Augusto Visintin,et al. Strong convergence results related to strict convexity , 1984 .
[6] Adrian J. Lew,et al. Discontinuous Galerkin methods for non‐linear elasticity , 2006 .
[7] G. Burton. Sobolev Spaces , 2013 .
[8] G. Knowles,et al. Finite element approximation to singular minimizers, and applications to cavitation in non-linear elasticity , 1987 .
[9] G. Buttazzo,et al. Interpretation of the Lavrentiev phenomenon by relaxation , 1992 .
[10] B. Dacorogna. Direct methods in the calculus of variations , 1989 .
[11] Zhipping Li. Element removal method for singular minimizers in variational problems involving Lavrentiev phenomenon , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.
[12] Examples of the Lavrentiev Phenomenon with Continuous Sobolev Exponent Dependence , 2003 .
[13] J. Ball. Foundations of Computational Mathematics: Singularities and computation of minimizers for variational problems , 2001 .
[14] Christoph Ortner,et al. On the Convergence of Adaptive Non-Conforming Finite Element Methods , 2008 .
[15] L. Evans. Measure theory and fine properties of functions , 1992 .
[16] John M. Ball,et al. One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation , 1985 .
[17] Michel Fortin,et al. Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.
[18] J. Ball,et al. A numerical method for detecting singular minimizers , 1987 .
[19] M. Lavrentieff,et al. Sur quelques problèmes du calcul des variations , 1927 .
[20] P. Raviart,et al. Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .
[21] Pablo V. Negrón Marrero. A numerical method for detecting singular minimizers of multidimensional problems in nonlinear elasticity , 1990 .
[22] OX St.Giles'Oxford. Singularities and Computation of Minimizers for Variational Problems , 2022 .
[23] Yu Bai,et al. A TRUNCATION METHOD FOR DETECTING SINGULAR MINIMIZERS INVOLVING THE LAVRENTIEV PHENOMENON , 2006 .
[24] Dietrich Braess. Finite Elements: Introduction , 2007 .
[25] A. Buffa,et al. Compact embeddings of broken Sobolev spaces and applications , 2009 .