Projects per year
In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady nonlinear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes. This is achieved by combining two key ingredients devised at the local level: a gradient reconstruction and a high-order stabilization term that generalizes the one originally introduced in the linear case. The convergence analysis is carried out using a compactness technique. Extending this technique to HHO methods has prompted us to develop a set of discrete functional analysis tools whose interest goes beyond the specific problem and method addressed in this work: (direct and) reverse Lebesgue and Sobolev embeddings for local polynomial spaces, Lp-stability and Ws,p-approximation properties for L2-projectors on such spaces, and Sobolev embeddings for hybrid polynomial spaces. Numerical tests are presented to validate the theoretical results for the original method and variants thereof.
|Number of pages||33|
|Journal||Mathematics of Computation|
|Publication status||Published - 2017|
- Convergence analysis
- Discrete functional analysis
- Hybrid High-Order methods
- Nonlinear elliptic equations
- W-approximation properties of L-projection on polynomials
- 1 Finished
Discrete functional analysis: bridging pure and numerical mathematics
Droniou, J., Eymard, R. & Manzini, G.
Australian Research Council (ARC), Monash University, Université Paris-Est Créteil Val de Marne (Paris-East Créteil University Val de Marne), University of California System
1/01/17 → 31/12/20