A finite element method is proposed and analyzed for non-divergence elliptic PDEs and HJB equations, proving well-posedness in W^{2,p} and optimal convergence for p up to 2 on convex domains while relaxing prior continuity requirements on coefficients.
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Analysis of a finite element method for second order uniformly elliptic PDEs in non-divergence form
A finite element method is proposed and analyzed for non-divergence elliptic PDEs and HJB equations, proving well-posedness in W^{2,p} and optimal convergence for p up to 2 on convex domains while relaxing prior continuity requirements on coefficients.