Hybrid high-order methods for the elliptic obstacle problem (Q2307428)

The authors introduce hybrid high-order methods for 2D and 3D obstacle problems. The methods are formulated in terms of face unknowns which are polynomials of degree \(k = 0\) or \(k = 1\) and in terms of cell unknowns which are polynomials of degree \(l = 0\). The discrete obstacle constraints are enforced on the cell unknowns. A priori error estimates are derived. For instance, if \(k = 1\), the method employs a local quadratic reconstruction operator and achieves an energy-error estimate of order \(h^{3/2-\varepsilon}\), \(\varepsilon>0\). Various numerical experiments are presented in order to illustrate the theoretical findings.