Method of moving frames to solve conservation laws on curved surfaces

DOI10.1007/s10915-011-9570-7zbMath1273.65138OpenAlexW2044330089MaRDI QIDQ357811

Sehun Chun

Publication date: 13 August 2013

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

Full work available at URL: https://doi.org/10.1007/s10915-011-9570-7

zbMATH Keywords

conservation lawdiscontinuous Galerkin methodsmethod of moving framesirregular closed surfacenonconvex closed surfaceopen sand closed pherical shellsPDEs on curved surfaces

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Hyperbolic equations on manifolds (58J45)

Related Items

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 ⋮ A meshfree collocation scheme for surface differential operators on point clouds ⋮ 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 ⋮ Method of moving frames to solve (an)isotropic diffusion equations on curved surfaces

Uses Software

• PPM
• chammp
• Nektar++

Cites Work

• 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
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• Polynomial interpolation results in Sobolev spaces
• Lagrange-Galerkin methods on spherical geodesic grids
• A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations.
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• Convergence of discrete Laplace-Beltrami operators over surfaces
• Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
• Transport and diffusion of material quantities on propagating interfaces via level set methods.
• A wave propagation algorithm for hyperbolic systems on curved manifolds
• 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
• An h-narrow band finite-element method for elliptic equations on implicit surfaces
• Diffusion Processes on Manifolds
• The chemical basis of morphogenesis
• Spectral/hp Element Methods for Computational Fluid Dynamics
• Variational problems and partial differential equations on implicit surfaces
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