Finite element approximation of nonlinear elliptic problems with discontinuous coefficients

On the Finite Element Analysis of Problems with Nonlinear Newton Boundary Conditions in Nonpolygonal Domains

“…(In the previous papers only strict monotonicity was established.) However, in contrast to standard nonlinear situations treated, e.g., in [2], [11], [12], [18], [28], where strong monotonicity was used, here we do not get an optimal O(h) error estimate for linear finite elements. The order of convergence is reduced due to the fact that only uniform monotonicity with growth of degree t 2+α , α > 0, holds now, and due to the nonlinearity in the boundary integrals.…”

“…Therefore, we introduce the concept of the so-called ideal triangulation, using the ideas from [30], [5], [11], [12], [13], [28], [29]. First we introduce the ideal triangle.…”

“…As a fundamental literature we mention [3] and [4]. The finite element variational crimes in the approximations of nonlinear elliptic problems were investigated in [12], [13], [7], [11], [24], [28] and [29]. The main tools were Zlámal's concepts of ideal triangulation and ideal interpolation ( [30]).…”

Finite Volume Method for 2D Linear and Nonlinear Elliptic Problems with Discontinuities

“…This kind of transmission (or bimaterial) problems were, for instance, studied in the finite element framework in [11,20] for p = 2 and in [17,18] for p = 2.…”

Semiregular Finite Elements in Solving Some Nonlinear Problems

“…ÈÖÓÓ . In the proof we use a modification of the trick with the use of Green's theorem introduced in [3], Theorem 3.2.5. By the definitions of a h ( u, w) and L h (w) we have…”