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Minimal residual discretization of a class of fully nonlinear elliptic PDE

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This research introduces finite-element methods for elliptic PDEs, suggesting convergence of Galerkin methods.

Convergence of $C^{1}$ conforming and discontinuous Galerkin methods is proven in the $L^{^ ext{∞}}$ norm.
The minimal residual principle utilizes the Alexandrov–Bakelman–Pucci estimate as its foundation.
Numerical experiments showcase adaptive mesh refinement driven by local residual information.
Results demonstrate effectiveness in both two and three space dimensions.

Gallistl et al. (2025) studied this question.

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