In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...

In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...

In the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain boundaries and the boundary nodes which are used in the traditional finite element method for the application of boundary condit...

the present study is concerned with optimal shape determination of inhomogeneous and temperature dependent domains under steady state heat conduction. such situations are important in many thermal design problems, especially in shape design of electronic components and chips. in the present paper, we formulate the shape optimization problem based on volume minimization of heat conductive materi...

An immersed enriched finite element method is proposed for the analysis of phononic crystals (PnCs) with (FE) meshes that are completely decoupled from geometry. Particularly, a technique to prescribe Bloch–Floquet periodic boundary conditions strongly on non-matching edges unit cell (PUC). The formulation effectively transforms non-confirming discretization into an node-to-node discretizations...

In this paper, a new derivation of a uniformly-convergent, second-order method for singularly-perturbed, linear ordinary differential equations based on the freezing of the coefficients of the differential equation, and integration of the resulting equations subject to continuity and smoothness conditions at the nodes, is presented. The derivation presented here is compared with others based on...

We consider grid approximations of a boundary value problem for the boundary layer equations modeling flow along a flat plate in a region excluding a neighbourhood of the leading edge. The problem is singularly perturbed with the perturbation parameter ε = 1/Re multiplying the highest derivative. Here the parameter ε takes any values from the half-interval (0,1], and Re is the Reynolds number. ...