
Divergence–free Scott–Vogelius elements on curved domains
We construct and analyze an isoparametric finite element pair for the St...
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A pressurerobust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators
The embedded discontinuous Galerkin (EDG) finite element method for the ...
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A lowdegree strictly conservative finite element method for incompressible flows
In this paper, a new P_2P_1 finite element pair is proposed for incompr...
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Numerical analysis of a discontinuous Galerkin method for the BorrvallPetersson topology optimization problem
Divergencefree discontinuous Galerkin (DG) finite element methods offer...
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The divergenceconforming immersed boundary method: Application to vesicle and capsule dynamics
We extend the recently introduced divergenceconforming immersed boundar...
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Highorder mixed finite elements for an energybased model of the polarization process in ferroelectric materials
An energybased model of the ferroelectric polarization process is prese...
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A divergenceconforming finite element method for the surface Stokes equation
The Stokes equation posed on surfaces is important in some physical mode...
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Divergencefree tangential finite element methods for incompressible flows on surfaces
In this work we consider the numerical solution of incompressible flows on twodimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the approximation of a velocity field that lies only in the tangential space of the given geometry. Abandoning H^1conformity allows us to construct finite elements which are – due to an application of the Piola transformation – exactly tangential. To reintroduce continuity (in a weak sense) we make use of (hybrid) discontinuous Galerkin techniques. To further improve this approach, H(div_Γ)conforming finite elements can be used to obtain exactly divergencefree velocity solutions. We present several new finite element discretizations. On a number of numerical examples we examine and compare their qualitative properties and accuracy.
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