In dentistry, many preparation guidelines for allceramic crowns are still based upon clinical experience and those developed for metal ceramic crowns that may not be applicable and need further experimental and numerical evaluation. Some specific features are requiring investigation in dental prosthetic devices, for example, configurations of the crowns’ margin [1], marginal thickness [2, 3] an...

In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of Nöther’s theorem from the formal variatio...

In this paper, a monolithic arbitrary Lagrangian–Eulerian (ALE)-finite element method (FEM) is developed based upon novel ALE mapping for type of parabolic/mixed parabolic moving interface problem with jump coefficients. A stable Stokes-pair mixed FEM within specific stabilization technique and time-difference scheme are to discretize in both semi- fully discrete fashion, which the stability er...

and this problem can be solved analytically: u (x) = x − sinhx/sinh1. The purpose of starting with this problem is to demonstrate the fundamental concepts and pitfalls in FEM in a situation where we know the correct answer, so that we will know where our approximation is good and where it is poor. In cases of practical interest we will look at ODEs and PDEs that are too complex to be solved ana...

Finite element methods are based on the variational formulation of partial differential equations which only need to compute the gradient of a function. Although unknowns are still associated to nodes, the function composed by piece-wise polynomials on each element and thus the gradient can be computed element-wise. Finite element spaces can thus be constructed on general triangulations and thi...

In this paper, we present a meshless method belonging to the family of element-free Galerkin (EFG) methods. The presented allows accurate enforcement essential boundary conditions. uses total Lagrangian formulation with explicit time integration facilitate code simplicity and robust computations in applications that involve large deformations non-linear materials. We use regularized weight func...

This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell’s equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete different...

An adaptive finite element method for solving incompressible steady-state free surfaces flow problems, driven by surface tension, is presented. Eulerian free surface capturing, the pseudo-concentration technique, is used to locate interfaces. This approach adds a transport equation to the Navier-Stokes equations. This system of equations is solved in a coupled manner using stabilized finite ele...