Hybridizable discontinuous Galerkin methods for the two-dimensional Monge-Ampère equation

DOI10.1007/s10915-024-02604-3MaRDI QIDQ6592266

Jaime Peraire, Ngoc Cuong Nguyen

Publication date: 24 August 2024

Published in: Journal of Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

elliptic equationsMonge-Ampère equationgrid adaptivity\(r\)-adaptivityhybridizable discontinuous Galerkin methods

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Boundary value problems for second-order elliptic equations (35J25) Fixed-point theorems (47H10) Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Monge-Ampère equations (35J96)

Cites Work

• Unnamed Item
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• A hybridizable discontinuous Galerkin method combined to a Schwarz algorithm for the solution of 3d time-harmonic Maxwell's equation
• Numerical solution of the optimal transportation problem using the Monge-Ampère equation
• Fast three dimensional r-adaptive mesh redistribution
• Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics
• A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains
• Optimal mass transport for higher dimensional adaptive grid generation
• Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
• Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
• A comparison of HDG methods for Stokes flow
• An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations
• A hybridizable discontinuous Galerkin method for Stokes flow
• Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations
• The geometry of r-adaptive meshes generated using optimal transport methods
• Hybridizable discontinuous Galerkin projection methods for Navier-Stokes and Boussinesq equations
• Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation
• Shock capturing with PDE-based artificial viscosity for DGFEM. I: Formulation
• A hybridizable discontinuous Galerkin method for fractional diffusion problems
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization
• An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations
• An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations
• Nonstandard local discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic equations in high dimensions
• Hybridized discontinuous Galerkin methods for wave propagation
• A hybridizable discontinuous Galerkin formulation for non-linear elasticity
• The hybridized discontinuous Galerkin method for implicit large-eddy simulation of transitional turbulent flows
• A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• A hybridizable discontinuous Galerkin method for both thin and 3D nonlinear elastic structures
• A finite element/operator-splitting method for the numerical solution of the two dimensional elliptic Monge-Ampère equation
• Symplectic Hamiltonian finite element methods for electromagnetics
• Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations
• An algorithm for stabilizing hybridizable discontinuous Galerkin methods for nonlinear elasticity
• Domain decomposition parabolic Monge-Ampère approach for fast generation of adaptive moving meshes
• Symplectic Hamiltonian finite element methods for linear elastodynamics
• A finite element/operator-splitting method for the numerical solution of the three dimensional Monge-Ampère equation
• Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows
• Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type
• A class of embedded discontinuous Galerkin methods for computational fluid dynamics
• Finite element approximations of general fully nonlinear second order elliptic partial differential equations based on the vanishing moment method
• Finite element approximations of the three dimensional Monge-Ampère equation
• Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations
• Superconvergent HDG methods for linear elasticity with weakly symmetric stresses
• A least-squares method for the numerical solution of the Dirichlet problem for the elliptic monge − ampère equation in dimension two
• A Finite Element Method for Nonlinear Elliptic Problems
• A Monge--Ampère-Solver for Free-Form Reflector Design
• A Numerical Method for the Elliptic Monge--Ampère Equation with Transport Boundary Conditions
• Standard finite elements for the numerical resolution of the elliptic Monge–Ampère equation: classical solutions
• Analysis of an HDG method for linear elasticity
• Hybridizable Discontinuous Galerkin Methods
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
• Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
• A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
• Analysis of HDG methods for Stokes flow
• The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow
• Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• Two Numerical Methods for the elliptic Monge-Ampère equation
• On Finite Element Methods for Fully Nonlinear Elliptic Equations of Second Order
• A hybridizable discontinuous Galerkin method for linear elasticity
• Polar factorization and monotone rearrangement of vector‐valued functions
• An HDG method for linear elasticity with strong symmetric stresses
• Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements
• Numerical comparison of hybridized discontinuous Galerkin and finite volume methods for incompressible flow
• Mixed interior penalty discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic equations in high dimensions
• Convergent Semi-Lagrangian Methods for the Monge--Ampère Equation on Unstructured Grids
• Implicit hybridized discontinuous Galerkin methods for compressible magnetohydrodynamics

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