How to adaptively resolve evolutionary singularities in differential equations with symmetry

DOI10.1007/s10665-009-9343-6zbMath1204.35016OpenAlexW2111082779MaRDI QIDQ976805

J. Martínez

Publication date: 16 June 2010

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10665-009-9343-6

zbMATH Keywords

interfaces\texttt{Matlab}\(r\)-adaptivityblow-up singularities

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) Theoretical approximation in context of PDEs (35A35) Geometric theory, characteristics, transformations in context of PDEs (35A30) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (13)

Asymptotic properties of the space-time adaptive numerical solution of a nonlinear heat equation ⋮ On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control ⋮ A spectral analysis of the nonlinear Schrödinger equation in the co-exploding frame ⋮ The quenching set of a MEMS capacitor in two-dimensional geometries ⋮ Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems ⋮ An asymptotic study of blow up multiplicity in fourth order parabolic partial differential equations ⋮ Adaptive Solution to Two-Dimensional Partial Differential Equations in Curved Domains Using the Monge--Ampére Equation ⋮ On the quenching behaviour of a semilinear wave equation modelling MEMS technology ⋮ Moving mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems ⋮ Similarity: Generalizations, applications and open problems ⋮ 3D Euler equations and ideal MHD mapped to regular systems: probing the finite-time blowup hypothesis ⋮ (In-)stability of singular equivariant solutions to the Landau–Lifshitz–Gilbert equation ⋮ Generic self-similar blowup for equivariant wave maps and Yang-Mills fields in higher dimensions

Uses Software

• Matlab
• DASSL
• MOVCOL4
• MOVCOL

Cites Work

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• Precise computations of chemotactic collapse using moving mesh methods
• An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization
• On the evolution of harmonic mappings of Riemannian surfaces
• New self-similar solutions of the nonlinear Schrödinger equation with moving mesh computations
• A moving collocation method for solving time dependent partial differential equations
• Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation
• Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
• Long-wave instabilities and saturation in thin film equations
• Stability of Moving Mesh Systems of Partial Differential Equations
• Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
• Blowup and dissipation in a critical-case unstable thin film equation
• Adaptive Geometric Integrators for Hamiltonian Problems with Approximate Scale Invariance
• 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
• Multibump, Blow-Up, Self-Similar Solutions of the Complex Ginzburg--Landau Equation
• On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
• An efficient dynamically adaptive mesh for potentially singular solutions
• Scaling invariance and adaptivity

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