An Immersed Weak Galerkin Method for Elliptic Interface Problems on Polygonal Meshes

@article{Park2022AnIW,
  title={An Immersed Weak Galerkin Method for Elliptic Interface Problems on Polygonal Meshes},
  author={Hyeokjoo Park and Do Young Kwak},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.07542}
}
. In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on each edge and broken linear polynomials satisfying the interface conditions in each element. For triangular meshes, such broken linear plynomials coincide with the basis functions in immersed finite element methods [26]. We establish some approximation… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 48 REFERENCES

An immersed weak Galerkin method for elliptic interface problems

  • Lin MuXu Zhang
  • Computer Science, Mathematics
    J. Comput. Appl. Math.
  • 2019

A weak Galerkin mixed finite element method for second order elliptic problems

The WG-MFEM is capable of providing very accurate numerical approximations for both the primary and flux variables and allowing the use of discontinuous approximating functions on arbitrary shape of polygons/polyhedra makes the method highly flexible in practical computation.

An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators

An arbitrary-order primal method for diffusion problems on general polyhedral meshes based on a local (elementwise) discrete gradient reconstruction operator that is proved to optimally converge in the energy norm and in the L2-norm of the potential for smooth solutions.

A weak Galerkin finite element method for the stokes equations

A weak Galerkin (WG) finite element method for the Stokes equations in the primal velocity-pressure formulation is introduced, equipped with stable finite elements consisting of usual polynomials of degree k≥1 for the velocity and polynoms of degrees k−1 forThe pressure, both are discontinuous.

A finite element method for interface problems in domains with smooth boundaries and interfaces

It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation.

A rectangular immersed finite element space for interface problems

Numerical results are presented to show the convergence of the Galerkin method based on an immersed finite element space for boundary value problems of partial differential equations with discontinuous coefficients.

An Analysis of a Broken P1-Nonconforming Finite Element Method for Interface Problems

An immersed finite element method based on the “broken” piecewise linear polynomials on interface triangular elements having edge averages as degrees of freedom is introduced and optimal error estimates of velocity and pressure are shown in this mixed finite volume method.

A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries

It is proved that the natural extension of this finite element approximation to the original domain is optimal-order accurate.