Two C0 least-squares FEMs (standard L2 and mesh-weighted) are proposed for non-divergence elliptic equations, with optimal a priori/a posteriori error estimates proved under a unique-solution assumption and tested numerically on smooth, non-smooth, and degenerate cases.
Ku , A remark on the coercivity for a first-order least-squares method , Numer
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Adaptive First-Order System Least-Squares Finite Element Methods for Second Order Elliptic Equations in Non-Divergence Form
Two C0 least-squares FEMs (standard L2 and mesh-weighted) are proposed for non-divergence elliptic equations, with optimal a priori/a posteriori error estimates proved under a unique-solution assumption and tested numerically on smooth, non-smooth, and degenerate cases.