The Lagrange-Galerkin spectral element method for the two-dimensional shallow water equations is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the nonlinearities introduced by the advection operator o...

The sclera is considered as the principal load-bearing tissue within eye. negatively charged; thus, it exhibits mechanical response to electrical stimulation. We recently demonstrated electroactive behavior of by performing experimental measurements that captured deformation tip scleral strips subjected electric voltage. also numerically analyzed electromechanical using a chemo-electro-mechanic...

SUMMARY We study different variants of the augmented Lagrangian-based block triangular preconditioner introduced by the first two authors in [SIAM J. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual (GMRES) method applied to various finite element and MAC discretizations of the Oseen problem in two and three space dimensions. Both steady and unstead...

We present a new algorithm to solve the problem of rock deformation. The method is based on a ‘classical’ Lagrangian finite element solver in which the connectivity between the nodes of the numerical mesh is updated at the end of each time (or deformation) step. The method, which we term Dynamic Lagrangian Remeshing (DLR), relies on the theory of Delaunay triangulation and produces optimal fini...

this research work is devoted to the development of a mathematical model for the simulation of the flow of polymeric melts through the die region of extruders. a set of governing equations are solved using finite element method. standard galerkin technique is used in conjunction with the mixed scheme to solve the flow equation. due to the non-linear nature of global equations, the picard iterat...

by minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. this new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. in fact, bot...