This analysis reveals new Sobolev-Poincaré inequalities for piecewise W^{1,p} functions on polytopic meshes, suggesting applications in nonlinear problem discretization.
We establish Sobolev-Poincar\'e inequalities for piecewise W1,p functions over sequences of fairly general polytopic (thence also shape-regular simplicial and Cartesian) meshes in any dimension; amongst others, they cover the case of standard Poincar\'e inequalities for piecewise W1,p functions and can be useful in the analysis of nonconforming finite element discretizations of nonlinear problems. Crucial tools in their derivation are novel Sobolev-trace inequalities and Babu ska-Aziz inequalities with mixed boundary conditions. We provide estimates that are constant free, i.e., that are fully explicit with respect to the geometric properties of the domain and the underlying sequence of polytopic meshes.
No takes yet. Share an insight, caveat, or question.
Botti et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: