## Discontinuous Galerkin immersed finite volume element method for anisotropic flow models in porous medium.(English)Zbl 1474.76040

Summary: By choosing the trial function space to the immersed finite element space and the test function space to be piecewise constant function space, we develop a discontinuous Galerkin immersed finite volume element method to solve numerically a kind of anisotropic diffusion models governed by the elliptic interface problems with discontinuous tensor-conductivity. The existence and uniqueness of the discrete scheme are proved, and an optimal-order energy-norm estimate and $$L^2$$-norm estimate for the numerical solution are derived.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 76S05 Flows in porous media; filtration; seepage

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### References:

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