Discrete ABP Estimate and Convergence Rates for Linear Elliptic Equations in Non-divergence Form

Ricardo H. Nochetto, Wujun Zhang

We design a two-scale finite element method (FEM) for linear elliptic PDEs in non-divergence form $A(x):D^{2}u(x)=f(x)$ in a bounded but not necessarily convex domain $\Omega$ and st…