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Neilan, Michael; Wu, Mohan
Journal of computational and applied mathematics, 08/2019, Letnik: 356Journal Article
In this article, we construct simple and convergent finite element methods for linear and nonlinear elliptic differential equations in non-divergence form with discontinuous coefficients. The methods are motivated by discrete Miranda–Talenti estimates, which relate the H2 semi-norm of piecewise polynomials with the L2 norm of its Laplacian on convex domains. We develop a stability and convergence theory of the proposed methods, and back up the theory with numerical experiments.
