Displaying similar documents to “Finite element solution of nonlinear elliptic equations with discontinuous coefficients and approximations in Sobolev-Slobodeckij spaces”

Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type

Liping Liu, Michal Křížek, Pekka Neittaanmäki (1996)

Applications of Mathematics

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A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree k ≥ 1 we prove the optimal rates of convergence 𝒪 ( h k ) in the H 1 -norm and 𝒪 ( h k + 1 ) in the L 2 -norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken...

On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients

Petr Harasim (2011)

Applications of Mathematics

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We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the...