Nonlinear analysis for the polygonal element

A New Stress Based Approach for Nonlinear Finite Element Analysis

This article demonstrates a new approach for nonlinear finite element analysis. The methodology is very suitable and gives very accurate results in linear as well as in nonlinear range of the material behavior. Proposed methodology can be regarded as stress based finite element analysis as it is required to define the stress distribution within the structural body with structural idealization a...

Nonlinear Continuum Mechanics for Finite Element Analysis

Well-posedness, Regularity, and Finite Element Analysis for the Axisymmetric Laplace Operator on Polygonal Domains

Let L := −r−2(r∂r)2 − ∂2 z . We consider the equation Lu = f on a bounded polygonal domain with suitable boundary conditions, derived from the three-dimensional axisymmetric Poisson’s equation. We establish the well-posedness, regularity and Fredholm results in weighted Sobolev spaces, for possible singular solutions caused by the singular coefficient of the operator L, as r → 0, and by non-smo...

Analysis of the Finite Element Method for Transmission/mixed Boundary Value Problems on General Polygonal Domains

We study theoretical and practical issues arising in the implementation of the Finite Element Method for a strongly elliptic second order equation with jump discontinuities in its coefficients on a polygonal domain Ω that may have cracks or vertices that touch the boundary. We consider in particular the equation − div(A∇u) = f ∈ H(Ω) with mixed boundary conditions, where the matrix A has variab...

Finite element analysis for the axisymmetric Laplace operator on polygonal domains

Let L := −r−2(r∂r )2 − ∂2 z . We consider the equation Lu = f on a bounded polygonal domain with suitable boundary conditions, derived from the three-dimensional axisymmetric Poisson’s equation. We establish the well-posedness, regularity, and Fredholm results in weighted Sobolev spaces, for possible singular solutions caused by the singular coefficient of the operator L, as r → 0, and by non-s...