Adaptive Solution to Two-Dimensional Partial Differential Equations in Curved Domains Using the Monge--Ampére Equation

Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06) Moving boundary problems for PDEs (35R37) Monge-Ampère equations (35J96)

Uses Software

MOVCOL4
MOVCOL

Cites Work

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Numerical solution of the optimal transportation problem using the Monge-Ampère equation
Regularized model of post-touchdown configurations in electrostatic MEMS: bistability analysis
Moving mesh methods with upwinding schemes for time-dependent PDEs
A study on moving mesh finite element solution of the porous medium equation
Finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains
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Influence of several factors in the generalized finite difference method
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Moving mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain
Monge-Ampère based moving mesh methods for numerical weather prediction, with applications to the Eady problem
Solving parabolic and hyperbolic equations by the generalized finite difference method
Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundaries
Regularized model of post-touchdown configurations in electrostatic MEMS: interface dynamics
Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis
A Numerical Method for the Elliptic Monge--Ampère Equation with Transport Boundary Conditions
Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
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Adaptivity with moving grids
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An Unconditionally Stable Convergent Finite Difference Method for Navier–Stokes Problems on Curved Domains
The finite difference method at arbitrary irregular grids and its application in applied mechanics
Polar factorization and monotone rearrangement of vector‐valued functions
Stability of Moving Mesh Systems of Partial Differential Equations
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
On the second boundary value problem for equations of Monge-Ampère type.
Convergent Filtered Schemes for the Monge--Ampère Partial Differential Equation
Measuring Mesh Qualities and Application to Variational Mesh Adaptation
MOVCOL4: A Moving Mesh Code for Fourth‐Order Time‐Dependent Partial Differential Equations
Parabolic Monge–Ampère methods for blow-up problems in several spatial dimensions
Adaptive mesh movements -- the MMPDE approach and its applications
An efficient dynamically adaptive mesh for potentially singular solutions
Scaling invariance and adaptivity

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