Abstract
The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis).
Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.
Abstract
In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in
ℝ
N
{\mathbb{R}^{N}}
involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential.
Using variational methods, we investigate the attainability of the corresponding minimization problem, and then obtain the existence of solutions.
We also consider another Choquard type equation involving the p-Laplacian and critical nonlinearities in
ℝ
N
{\mathbb{R}^{N}}
.
Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity
