# Error estimation for second-order PDEs in non-variational form

@article{Blechschmidt2019ErrorEF, title={Error estimation for second-order PDEs in non-variational form}, author={Jan Blechschmidt and Roland Herzog and Max Winkler}, journal={ArXiv}, year={2019}, volume={abs/1909.12676} }

Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or as the linearization of fully nonlinear second-order PDEs. The non-divergence form in these problems is natural. If the coefficients of the diffusion matrix are not differentiable, the problem can not be transformed into the more convenient variational form…

## 3 Citations

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An abstract framework for the a priori error analysis of a broad family of numerical methods is introduced and the quasi-optimality of discrete approximations under three key conditions of Lipschitz continuity, discrete consistency and strong monotonicity of the numerical method is proved.

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We prove the convergence of adaptive discontinuous Galerkin and $C^0$-interior penalty methods for fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs equations with Cordes…

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