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math.NA2025
Analysis of a Discontinuous Galerkin Method for Diffusion Problems on Intersecting Domains
Miroslav Kuchta, Rami Masri, Beatrice Riviere
The interior penalty discontinuous Galerkin method is applied to solve elliptic equations on either networks of segments or networks of planar surfaces, with arbitrary but fixed nu…
math.NA2023
Discontinuous Galerkin methods for 3D-1D systems
Rami Masri, Miroslav Kuchta, Beatrice Riviere
We propose and analyze discontinuous Galerkin (dG) approximations to 3D-1D coupled systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D cente…
math.NA2023
Bound-preserving discontinuous Galerkin methods for compressible two-phase flows in porous media
M. S. Joshaghani, B. Riviere
This paper presents a numerical study of immiscible, compressible two-phase flows in porous media, that takes into account heterogeneity, gravity, anisotropy, and injection/product…