Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems
From MaRDI portal
Publication:1695359
DOI10.1016/j.jcp.2017.08.032zbMath1380.65152OpenAlexW2752836011MaRDI QIDQ1695359
Alan E. Lindsay, Kelsey L. DiPietro
Publication date: 7 February 2018
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2017.08.032
PDEs in connection with optics and electromagnetic theory (35Q60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Blow-up in context of PDEs (35B44) Higher-order parabolic systems (35K41)
Related Items (2)
Adaptive Solution to Two-Dimensional Partial Differential Equations in Curved Domains Using the Monge--Ampére Equation ⋮ Moving mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The quenching set of a MEMS capacitor in two-dimensional geometries
- Regularized model of post-touchdown configurations in electrostatic MEMS: bistability analysis
- An efficient approach for the numerical solution of the Monge-Ampère equation
- Curvature driven flow of bi-layer interfaces
- Analysis of Galerkin methods for the fully nonlinear Monge-Ampère equation
- Moving mesh methods with upwinding schemes for time-dependent PDEs
- The geometry of r-adaptive meshes generated using optimal transport methods
- Quadratic mixed finite element approximations of the Monge-Ampère equation in 2D
- 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
- Stability and dynamics of self-similarity in evolution equations
- How to adaptively resolve evolutionary singularities in differential equations with symmetry
- Semi-implicit level set methods for curvature and surface diffusion motion
- Dynamics of three-dimensional thin film rupture
- Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem
- The problem of blow-up in nonlinear parabolic equations
- Finite-time thin film rupture driven by modified evaporative loss
- A semi-implicit moving mesh method for the focusing nonlinear Schrödinger equation
- Optimal mass transport-based adaptive mesh method for phase-field models of two-phase fluid flows
- On the semilinear elliptic equations of electrostatic NEMS devices
- An asymptotic study of blow up multiplicity in fourth order parabolic partial differential equations
- Monge-Ampère based moving mesh methods for numerical weather prediction, with applications to the Eady problem
- On the partial differential equations of electrostatic MEMS devices with effects of Casimir force
- Mathematical Modeling of Electrostatic MEMS with Tailored Dielectric Properties
- Regularized model of post-touchdown configurations in electrostatic MEMS: interface dynamics
- Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis
- The Stability and Evolution of Curved Domains Arising from One-Dimensional Localized Patterns
- Self-Similar Voiding Solutions of a Single Layered Model of Folding Rocks
- Multiple Quenching Solutions of a Fourth Order Parabolic PDE with a Singular Nonlinearity Modeling a MEMS Capacitor
- Triple-deck analysis of transonic high Reynolds number flow through slender channels
- Stochastic Domain Decomposition for Time Dependent Adaptive Mesh Generation
- The Adaptive Verlet Method
- Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
- Stability of self-similar solutions for van der Waals driven thin film rupture
- Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains
- Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method
- Five types of blow-up in a semilinear fourth-order reaction–diffusion equation: an analytic–numerical approach
- Adaptivity with moving grids
- Polar factorization and monotone rearrangement of vector‐valued functions
- Mixed and Hybrid Finite Element Methods
- Refined asymptotics for the blowup of ut — δu = up
- Boundary regularity of maps with convex potentials
- Finite Element Methods for Elliptic Equations Using Nonconforming Elements
- Finite difference approximation of boundary conditions along irregular boundaries
- Stability of Moving Mesh Systems of Partial Differential Equations
- Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems
- A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
- Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing
- Numerical Solution of Partial Differential Equations
- Blow-up in a fourth-order semilinear parabolic equation from explosion-convection theory
- Self-Similar Blow-Up in Higher-Order Semilinear Parabolic Equations
- Exponential Asymptotics for Thin Film Rupture
- Measuring Mesh Qualities and Application to Variational Mesh Adaptation
- Discontinuous Galerkin methods for the biharmonic problem
- Geometric evolution of bilayers under the functionalized Cahn–Hilliard equation
- A diffuse-interface model for electrowetting drops in a Hele-Shaw cell
- 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
- Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties
- Adaptive mesh movements -- the MMPDE approach and its applications
- Moving mesh methods in multiple dimensions based on harmonic maps
- An efficient dynamically adaptive mesh for potentially singular solutions
- Scaling invariance and adaptivity
This page was built for publication: Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems
