Pointwise rates of convergence for the Oliker–Prussner method for the Monge–Ampère equation
暂无分享,去创建一个
[1] J. Mirebeau. Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams , 2015, 1503.00947.
[2] R. Nochetto,et al. Discrete ABP Estimate and Convergence Rates for Linear Elliptic Equations in Non-divergence Form , 2014, Foundations of Computational Mathematics.
[3] Jean-Marie Mirebeau,et al. Monotone and consistent discretization of the Monge-Ampère operator , 2014, Math. Comput..
[4] Quentin Mérigot,et al. Handling Convexity-Like Constraints in Variational Problems , 2014, SIAM J. Numer. Anal..
[5] Gerard Awanou,et al. Standard finite elements for the numerical resolution of the elliptic Monge–Ampère equation: classical solutions , 2013, 1310.4576.
[6] Gerard Awanou,et al. Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: Aleksandrov solutions , 2013, 1310.4568.
[7] Xiaobing Feng,et al. Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations , 2012, J. Comput. Appl. Math..
[8] S. C. Brenner,et al. Finite element approximations of the three dimensional Monge-Ampère equation , 2012 .
[9] S. C. Brenner,et al. {C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation , 2011 .
[10] Adam M. Oberman. A Numerical Method for Variational Problems with Convexity Constraints , 2011, SIAM J. Sci. Comput..
[11] Michael Holst,et al. Efficient mesh optimization schemes based on Optimal Delaunay Triangulations , 2011 .
[12] Susanne C. Brenner,et al. C0 penalty methods for the fully nonlinear Monge-Ampère equation , 2011, Math. Comput..
[13] Adam M. Oberman,et al. Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge-Ampère Equation in Dimensions Two and Higher , 2010, SIAM J. Numer. Anal..
[14] Adam M. Oberman,et al. Two Numerical Methods for the elliptic Monge-Ampère equation , 2010 .
[15] Adam M. Oberman,et al. Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation , 2010, J. Comput. Phys..
[16] Michael Neilan,et al. A nonconforming Morley finite element method for the fully nonlinear Monge-Ampère equation , 2010, Numerische Mathematik.
[17] Pedro Morin,et al. On Convex Functions and the Finite Element Method , 2008, SIAM J. Numer. Anal..
[18] Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian , 2008 .
[19] Klaus Böhmer,et al. On Finite Element Methods for Fully Nonlinear Elliptic Equations of Second Order , 2008, SIAM J. Numer. Anal..
[20] Xiaobing Feng,et al. Analysis of Galerkin Methods for the Fully Nonlinear Monge-Ampère Equation , 2007, J. Sci. Comput..
[21] Xiaobing Feng,et al. Mixed Finite Element Methods for the Fully Nonlinear Monge-Ampère Equation Based on the Vanishing Moment Method , 2007, SIAM J. Numer. Anal..
[22] Roland Glowinski,et al. Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type , 2006 .
[23] Roland Glowinski,et al. Numerical solution of the two-dimensional elliptic Monge–Ampère equation with Dirichlet boundary conditions: a least-squares approach , 2004 .
[24] Roland Glowinski,et al. Numerical solution of the two-dimensional elliptic Monge-Ampère equation with Dirichlet boundary conditions: an augmented Lagrangian approach , 2003 .
[25] Philippe Choné,et al. NON-CONVERGENCE RESULT FOR CONFORMAL APPROXIMATION OF VARIATIONAL PROBLEMS SUBJECT TO A CONVEXITY CONSTRAINT , 2001 .
[26] Bertrand Maury,et al. A numerical approach to variational problems subject to convexity constraint , 2001, Numerische Mathematik.
[27] Hung-Ju Kuo,et al. A note on the discrete Aleksandrov-Bakelman maximum principle , 2000 .
[28] Herbert Edelsbrunner,et al. Triangulations and meshes in computational geometry , 2000, Acta Numerica.
[29] Hung-Ju Kuo,et al. Positive difference operators on general meshes , 1996 .
[30] L. Caffarelli,et al. Fully Nonlinear Elliptic Equations , 1995 .
[31] P. Lions,et al. User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.
[32] N. Trudinger,et al. Discrete methods for fully nonlinear elliptic equations , 1992 .
[33] Barry Joe,et al. Construction of three-dimensional Delaunay triangulations using local transformations , 1991, Comput. Aided Geom. Des..
[34] G. Barles,et al. Convergence of approximation schemes for fully nonlinear second order equations , 1990, 29th IEEE Conference on Decision and Control.
[35] Hung-Ju Kuo,et al. Linear elliptic difference inequalities with random coefficients , 1990 .
[36] Vladimir Oliker,et al. On the numerical solution of the equation $$\frac{{\partial ^2 z}}{{\partial x^2 }}\frac{{\partial ^2 z}}{{\partial y^2 }} - \left( {\frac{{\partial ^2 z}}{{\partial x\partial y}}} \right)^2 = f$$ and its discretizations, I , 1989 .
[37] A. Figalli. On the Monge-Ampère equation , 2019 .
[38] Michael Neilan,et al. Quadratic Finite Element Approximations of the Monge-Ampère Equation , 2012, Journal of Scientific Computing.
[39] Xiaobing Feng,et al. Vanishing Moment Method and Moment Solutions for Fully Nonlinear Second Order Partial Differential Equations , 2009, J. Sci. Comput..
[40] Danny C. Sorensen,et al. A quadratically constrained minimization problem arising from PDE of Monge–Ampère type , 2009, Numerical Algorithms.
[41] R. Glowinski,et al. An augmented Lagrangian approach to the numerical solution of the Dirichlet problem for the elliptic Monge-Ampère equation in two dimensions. , 2006 .
[42] LongChen,et al. OPTIMAL DELAUNAY TRIANGULATIONS , 2004 .
[43] V. V. Buldygin,et al. Brunn-Minkowski inequality , 2000 .
[44] L. R. Scott,et al. The Mathematical Theory of Finite Element Methods , 1994 .
[45] L. Caffarelli. Interior $W^{2,p}$ estimates for solutions of the Monge-Ampère equation , 1990 .
[46] Luis A. Caffarelli,et al. A localization property of viscosity solutions to the Monge-Ampere equation and their strict convexity , 1990 .