Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements (Q4637678)

scientific article; zbMATH DE number 6864532

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English	Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements	scientific article; zbMATH DE number 6864532

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instance of

scholarly article

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title

Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements (English)

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SIAM Journal on Scientific Computing

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publication date

25 April 2018

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full work available at URL

https://arxiv.org/abs/1612.08077

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zbMATH Keywords

Monge-Ampère equation

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mesh adaptivity

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finite element

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optimal transport

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describes a project that uses

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On Convex Functions and the Finite Element Method

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Unified form language

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Quadratic mixed finite element approximations of the Monge-Ampère equation in 2D

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Q4356470

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Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem

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Two Numerical Methods for the elliptic Monge-Ampère equation

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Numerical solution of the optimal transportation problem using the Monge-Ampère equation

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A (dis)continuous finite element model for generalized 2D vorticity dynamics

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Polar factorization and monotone rearrangement of vector‐valued functions

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𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation

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Finite element approximations of the three dimensional Monge-Ampère equation

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Fast three dimensional r-adaptive mesh redistribution

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Composing Scalable Nonlinear Algebraic Solvers

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Monge-Ampère based moving mesh methods for numerical weather prediction, with applications to the Eady problem

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Adaptivity with moving grids

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The scaling and skewness of optimally transported meshes on the sphere

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The geometry of r-adaptive meshes generated using optimal transport methods

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Parabolic Monge–Ampère methods for blow-up problems in several spatial dimensions

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Moving Mesh Generation Using the Parabolic Monge–Ampère Equation

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Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution

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Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type

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An augmented Lagrangian approach to the numerical solution of the Dirichlet problem for the elliptic Monge-Ampère equation in two dimensions

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An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization

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Generalized Monge–Kantorovich Optimization for Grid Generation and Adaptation in $L_{p}$

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Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method

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Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation

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Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge–Ampère Equation in Dimensions Two and Higher

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A Parallel Edge Orientation Algorithm for Quadrilateral Meshes

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TSFC: A Structure-Preserving Form Compiler

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Adaptive moving mesh methods

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Modelling atmospheric flows with adaptive moving meshes

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A Finite Element Method for Second Order Nonvariational Elliptic Problems

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A Finite Element Method for Nonlinear Elliptic Problems

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Numerical solution of the Monge--Ampère equation by a Newton's algorithm

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An Algorithm for the Optimization of Finite Element Integration Loops

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Preconditioning discretizations of systems of partial differential equations

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Polar factorization of maps on Riemannian manifolds

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Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements

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Finite element methods for fully nonlinear second order PDEs based on a discrete Hessian with applications to the Monge-Ampère equation

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On the numerical solution of the equation $\frac{\partial ^ 2z\partial ^ 2z}{\partial x^ 2\partial y^ 2}-(\frac{\partial ^ 2z}{\partial x\partial y})^ 2=f$ and its discretizations. I

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An all-scale anelastic model for geophysical flows: dynamic grid deformation.

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Firedrake

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Efficient implementation of essentially nonoscillatory shock-capturing schemes

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Towards mesh adaptivity for geophysical turbulence: continuous mapping approach

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Optimal mass transport for higher dimensional adaptive grid generation

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Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

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Identifiers

zbMATH Open document ID

1448.65143

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DOI

10.1137/16M1109515

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4637678