High-order method with moving frames to compute the covariant derivatives of vectors on general 2D curved surfaces

Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Cites Work

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High-order spectral/\(hp\) element discretisation for reaction-diffusion problems on surfaces: application to cardiac electrophysiology
Method of moving frames to solve conservation laws on curved surfaces
Method of moving frames to solve (an)isotropic diffusion equations on curved surfaces
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A finite element exterior calculus framework for the rotating shallow-water equations
A practical finite difference scheme for the Navier-Stokes equation on curved surfaces in \(\mathbb{R}^3\)
High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations
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A compatible and conservative spectral element method on unstructured grids
A standard test set for numerical approximations to the shallow water equations in spherical geometry
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Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces
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Reducing errors caused by geometrical inaccuracy to solve partial differential equations with moving frames on curvilinear domain
A finite element approach for vector- and tensor-valued surface PDEs
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Mesh generation in curvilinear domains using high‐order elements
On Covariant Derivatives and Their Applications to Image Regularization
Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics
Variational problems and partial differential equations on implicit surfaces

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