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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.19454 |
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| _version_ | 1866914579523567616 |
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| author | Etangsale, Gregory Fontaine, Vincent Younes, Anis |
| author_facet | Etangsale, Gregory Fontaine, Vincent Younes, Anis |
| contents | We derive a primal discontinuous Galerkin (DG) formulation for heterogeneous and anisotropic diffusion, obtained by exact algebraic elimination of the skeletal unknown in a compact hybridized interior penalty (H-IP) method. The resulting Unified Interior Penalty DG (UIP-DG) scheme involves transmissibility-based weights inherited from the hybrid formulation, together with two stabilization terms acting respectively on the primal jump and on the jump of the normal diffusive flux. These penalties scale, respectively, with the harmonic mean and with the inverse arithmetic mean of the face-wise transmissibilities. This construction provides a unified perspective on several interior penalty approaches previously introduced independently, while yielding a robust method with stability properties independent of the diffusion contrast and anisotropy. We prove consistency, coercivity, and boundedness of the formulation, and derive quasi-optimal energy-norm a priori error estimates for all variants. Numerical experiments confirm the theoretical claims. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Transmissibility-Based Interior Penalty DG Method for Heterogeneous and Anisotropic Diffusion Etangsale, Gregory Fontaine, Vincent Younes, Anis Numerical Analysis 65N30, 65N12, 65N15 We derive a primal discontinuous Galerkin (DG) formulation for heterogeneous and anisotropic diffusion, obtained by exact algebraic elimination of the skeletal unknown in a compact hybridized interior penalty (H-IP) method. The resulting Unified Interior Penalty DG (UIP-DG) scheme involves transmissibility-based weights inherited from the hybrid formulation, together with two stabilization terms acting respectively on the primal jump and on the jump of the normal diffusive flux. These penalties scale, respectively, with the harmonic mean and with the inverse arithmetic mean of the face-wise transmissibilities. This construction provides a unified perspective on several interior penalty approaches previously introduced independently, while yielding a robust method with stability properties independent of the diffusion contrast and anisotropy. We prove consistency, coercivity, and boundedness of the formulation, and derive quasi-optimal energy-norm a priori error estimates for all variants. Numerical experiments confirm the theoretical claims. |
| title | A Unified Transmissibility-Based Interior Penalty DG Method for Heterogeneous and Anisotropic Diffusion |
| topic | Numerical Analysis 65N30, 65N12, 65N15 |
| url | https://arxiv.org/abs/2605.19454 |