Abstract This work introduces finite-element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon the Alexandrov–Bakelman–Pucci estimate. Under rather general structural assumptions on the operator, convergence of C^1 conforming and discontinuous Galerkin methods is proven in the L^^ norm. Numerical experiments on the performance of adaptive mesh refinement driven by local information of the residual in two and three space dimensions are provided.
Gallistl et al. (Thu,) studied this question.
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