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Mixed Hybrid High-Order Methods for Sixth-Order Problems: Fully Non-conforming and C0-Conforming Discretizations

  • Arbaz Khan
  • Ajay Kumar
  • Harpal Singh
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Abstract

We consider a class of sixth-order elliptic partial differential equations in two and three dimensions subject to simply supported and Cahn--Hilliard-type boundary conditions. Based on the Ciarlet--Raviart reformulation, we recast the sixth-order problem as an equivalent mixed system involving second- and fourth-order equations and establish its well-posedness under suitable assumptions. For the resulting mixed formulation, we propose and analyse two discretization frameworks: a fully non-conforming hybrid high-order (HHO) method on general polytopal meshes and a C0-conforming HHO--finite element method on simplicial meshes. We prove stability and derive optimal-order a priori error estimates for the primary variables under appropriate regularity assumptions. For the fully non-conforming HHO method, we further derive a reliable residual-based a posteriori error estimator. Numerical experiments confirm the theoretical convergence rates and illustrate the robustness of the proposed methods for a range of mobility parameters.

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Cite

BibTeXRIS
BibTeX
@misc{khan2026mixed,
  title = {{Mixed Hybrid High-Order Methods for Sixth-Order Problems: Fully Non-conforming and $C^0$-Conforming Discretizations}},
  author = {Arbaz Khan and Ajay Kumar and Harpal Singh},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11167},
  eprint = {2609.11167},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11167},
}
RIS
TY  - UNPB
TI  - Mixed Hybrid High-Order Methods for Sixth-Order Problems: Fully Non-conforming and C^0-Conforming Discretizations
AU  - Arbaz Khan
AU  - Ajay Kumar
AU  - Harpal Singh
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11167
UR  - https://arxiv.org/abs/2609.11167
AB  - We consider a class of sixth-order elliptic partial differential equations in two and three dimensions subject to simply supported and Cahn--Hilliard-type boundary conditions. Based on the Ciarlet--Raviart reformulation, we recast the sixth-order problem as an equivalent mixed system involving second- and fourth-order equations and establish its well-posedness under suitable assumptions. For the resulting mixed formulation, we propose and analyse two discretization frameworks: a fully non-conforming hybrid high-order (HHO) method on general polytopal meshes and a C^0-conforming HHO--finite element method on simplicial meshes. We prove stability and derive optimal-order a priori error estimates for the primary variables under appropriate regularity assumptions. For the fully non-conforming HHO method, we further derive a reliable residual-based a posteriori error estimator. Numerical experiments confirm the theoretical convergence rates and illustrate the robustness of the proposed methods for a range of mobility parameters.
ER  -