C0 finite element approximations of linear elliptic equations in non-divergence form and Hamilton–Jacobi–Bellman equations with Cordes coefficients

This paper is concerned with C0 (non-Lagrange) finite element approximations of the linear elliptic equations in non-divergence form and Hamilton–Jacobi–Bellman (HJB) Cordes coefficients. Motivated by Miranda–Talenti estimate, a discrete analog proved once space on $$(n-1)$$ -dimensional subsimplex (face) $$C^1$$ $$(n-2)$$ subsimplex. The main novelty non-standard methods to introduce an interior stabilization term argument PDE-induced variational or HJB equations. As distinctive feature proposed methods, no parameter involved forms. consequence, coercivity constant (resp. monotonicity constant) for equations) at level exactly same as that from PDE theory. quasi-optimal order error estimates well convergence semismooth Newton method are established. Numerical experiments provided validate theory illustrate accuracy computational efficiency methods.