A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows

@article{DAngelo2009AFE,
  title={A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows},
  author={Carlo D'Angelo and Paolo Zunino},
  journal={SIAM J. Numer. Anal.},
  year={2009},
  volume={47},
  pages={3990-4020}
}
We propose a finite element scheme for the approximation of multidomain heterogeneous problems arising in the general framework of linear incompressible flows (e.g., Stokes' and Darcy's equations). We exploit stabilized mixed finite elements together with Nitsche-type matching conditions that automatically adapt to the coupling of different subproblem combinations. Optimal error estimates are derived for the coupled problem. Then, we propose and analyze an iterative splitting strategy for the… 

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References

SHOWING 1-10 OF 44 REFERENCES

Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations

A Galerkin Finite Element approximation of the Stokes–Darcy problem which models the coupling between surface and groundwater flows and an iterative subdomain method for its solution is proposed, inspired to the domain decomposition theory.

A unified stabilized method for Stokes' and Darcy's equations

A Domain Decomposition Method Based on Weighted Interior Penalties for Advection-Diffusion-Reaction Problems

The convergence of the resulting domain decomposition method is proved, and this result holds true uniformly with respect to the diffusion parameter, and the numerical scheme that is proposed here can be applied straightforwardly to diffusion- dominated, advection-dominated, and hyperbolic problems.

The Nitsche mortar finite‐element method for transmission problems with singularities

The paper deals with a Nitsche-type finite-element method for treating non-matching meshes at the interface of some domain decomposition for transmission problems of the plane with Dirichlet boundary conditions entailing singularities at the corners or endpoints of the polygonal interface.

A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems

A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems and it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.

Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling

The convergence of some iteration-by-subdomain methods based on Robin conditions on the interface are proved, and for suitable finite element approximations it is shown that the rate of convergence is independent of the mesh size.

hp-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form

A domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form that is well-suited for problems coupling hyperbolic and elliptic equations and proves an error bound which is optimal withrespect to the mesh-size and suboptimal with respect to the polynomial degree.

A finite element method for domain decomposition with non-matching grids

In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary

Continuous Interior Penalty Finite Element Method for Oseen's Equations

This paper presents an extension of the continuous interior penalty method of Douglas and Dupont to Oseen's equations, and proves energy-type a priori error estimates independent of the local Reynolds number.

A stabilized mixed discontinuous Galerkin method for Darcy flow