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- W2975962085 abstract "This paper establishes the optimal $H^1$-norm error estimate for a nonstandard finite element method for approximating $H^2$ strong solutions of second order linear elliptic PDEs in non-divergence form with continuous coefficients. To circumvent the difficulty of lacking an effective duality argument for this class of PDEs, a new analysis technique is introduced; the crux of it is to establish an $H^1$-norm stability estimate for the finite element approximation operator which mimics a similar estimate for the underlying PDE operator recently established by the authors and its proof is based on a freezing coefficient technique and a topological argument. Moreover, both the $H^1$-norm stability and error estimate also hold for the linear finite element method." @default.
- W2975962085 created "2019-10-03" @default.
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- W2975962085 date "2019-09-30" @default.
- W2975962085 modified "2023-09-26" @default.
- W2975962085 title "$H^1$-norm error estimate for a nonstandard finite element approximation of second-order linear elliptic PDEs in non-divergence form" @default.
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- W2975962085 doi "https://doi.org/10.48550/arxiv.1909.13803" @default.
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