Method of moving frames to solve (an)isotropic diffusion equations on curved surfaces

DOI10.1007/s10915-013-9775-zzbMath1306.65262OpenAlexW1999558859MaRDI QIDQ461258

Sehun Chun

Publication date: 10 October 2014

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

Full work available at URL: https://doi.org/10.1007/s10915-013-9775-z

zbMATH Keywords

convergenceerror estimatesRiemannian geometrynumerical examplesLaplace-Beltrami operatormethod of moving framesanisotropic diffusion-reaction equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (7)

Divergence/connection preservation scheme in the curvilinear domain with a small geometric approximation error ⋮ Reducing errors caused by geometrical inaccuracy to solve partial differential equations with moving frames on curvilinear domain ⋮ Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces ⋮ Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: applications to invisible cloak and ELF propagation ⋮ High-order method with moving frames to compute the covariant derivatives of vectors on general 2D curved surfaces ⋮ Relative acceleration of orthonormal basis vectors for the geometric conduction blocks of the cardiac electric signal propagation on anisotropic curved surfaces ⋮ \textit{Nektar}++: enhancing the capability and application of high-fidelity spectral/\(hp\) element methods

Uses Software

• PPM
• Nektar++

Cites Work

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• Method of moving frames to solve conservation laws on curved surfaces
• To CG or to HDG: A comparative study
• A Lagrangian particle method for reaction-diffusion systems on deforming surfaces
• How to simulate anisotropic diffusion processes on curved surfaces
• High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations
• An improvement of a recent Eulerian method for solving PDEs on general geometries
• Convergence of discrete Laplace-Beltrami operators over surfaces
• Transport and diffusion of material quantities on propagating interfaces via level set methods.
• Diffusion on a curved surface coupled to diffusion in the volume: application to cell biology
• Numerical solution of the reaction-advection-diffusion equation on the sphere
• Fourth order partial differential equations on general geometries
• A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• Semi-Implicit Time-Discretization Schemes for the Bidomain Model
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• A Proof of the Hairy Ball Theorem
• Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties
• The chemical basis of morphogenesis
• Fermi Normal Coordinates and Some Basic Concepts in Differential Geometry
• General linear methods
• Variational problems and partial differential equations on implicit surfaces

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