Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems

The relaxation in the calculus of variation motivates numerical analysis a class degenerate convex minimization problems with non-strictly energy densities some convexity control and two-sided $p$-growth. minimizers may be non-unique primal variable but lead to unique stress $\sigma \in H(\operatorname{div},\Omega;\mathbb{M})$. Examples include p-Laplacian, an optimal design problem topology optimization, convexified double-well problem. approximation by hybrid high-order methods (HHO) utilizes reconstruction gradients piecewise Raviart-Thomas or BDM finite elements without stabilization on regular triangulation into simplices. application this HHO method allows for $H(\operatorname{div})$ conforming $\sigma_h$. main results are a~priori posteriori error estimates $\sigma-\sigma_h$ Lebesgue norms computable lower bound. Numerical benchmarks display higher convergence rates polynomial degrees adaptive mesh-refining first superlinear guaranteed bounds.