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Higher‐order surface FEM for incompressible Navier‐Stokes flows on manifolds

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Outgoing claims: the papers this work cites, builds on, or argues with.

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Finite Element Methods for Flow Problems
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Benchmark Computations of Laminar Flow Around a Cylinder
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The Finite Element Analysis of Shells - Fundamentals
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Structural Shell Analysis
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The variational multiscale method for laminar and turbulent flow
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Finite Elements for the Beltrami operator on arbitrary surfaces
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On the Two-Phase Navier–Stokes Equations with Boussinesq–Scriven Surface Fluid
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On the Navier–Stokes equations on manifolds with curvature
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Dynamics of a fluid interface Equation of motion for Newtonian surface fluids
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High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
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Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
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A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations
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A new finite element formulation for computational fluid dynamics: VII. The stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
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Two classes of mixed finite element methods
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A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations
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A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations
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A numerical solution of the Navier-Stokes equations using the finite element technique
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Interfacial Transport Processes and Rheology
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A finite element method for the simulation of strong and weak discontinuities in solid mechanics
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Finite element modeling of a linear membrane shell problem using tangential differential calculus
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Higher-order meshing of implicit geometries—Part I: Integration and interpolation in cut elements
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Higher-order meshing of implicit geometries, Part II: Approximations on manifolds
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Finite element stabilization parameters computed from element matrices and vectors
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The variational multiscale method—a paradigm for computational mechanics
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A finite element approach to incompressible two-phase flow on manifolds
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Finite element methods for surface PDEs
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On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers
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Solving the incompressible surface Navier-Stokes equation by surface finite elements
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Euler and Navier–Stokes equations on the hyperbolic plane
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Energetic variational approaches for incompressible fluid systems on an evolving surface
inferredcites →https://doi.org/10.1093/imanum/drt016openalex-snapshot
A stabilized finite element method for advection-diffusion equations on surfaces
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Analysis of trace finite element methods for surface partial differential equations
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Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
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Unfitted Finite Element Methods Using Bulk Meshes for Surface Partial Differential Equations
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A Higher Order Finite Element Method for Partial Differential Equations on Surfaces
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A Simple Mesh Generator in MATLAB
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Incompressible flow and the finite element method
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Solid Mechanics and Its Applications
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Groups of Diffeomorphisms and the Motion of an Incompressible Fluid
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Incompressible fluid problems on embedded surfaces: Modeling and variational formulations
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On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space
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On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Vorticity‐stream function approaches are inappropriate to solve the surface Navier‐Stokes equation on a torus
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