Three Maxwell eigensolvers are discussed in this paper. Two of them use classical nonconforming finite element approximations, and the other is an interior penalty type discontinuous Galerkin method. A main feature of these solvers is that they are based on the formulation of the Maxwell eigenproblem on the space H0(curl; Ω) ∩ H(div; Ω). These solvers are free of spurious eigenmodes and they do...

Abstract A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general sources allows quasi-best approximation lowest-order finite element methods. This paper establishes the stability a priori error control in piecewise energy weaker Sobolev norms under minimal hypotheses. Applications include stream function vorticity formulation of incompressible 2D Navier-...

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We present a C0 interior penalty finite element method for the sixth-order phase field crystal equation. demonstrate that numerical scheme is uniquely solvable, unconditionally energy stable, and convergent. remark novelty of this paper lies in fact first developed Additionally, error analysis presented develops detailed methodology analyzing time dependent problems utilizing method. furthermor...

Abstract — The main goal of this article is to investigate the numerical solution of a vector-valued nonlinear wave equation, the nonlinearity being of the Ginzburg-Landau type, namely (|~u|2 − 1)~u. This equation is obtained when treating by penalty a constrained wave-motion, where the displacement vector is of constant length (1 here, after rescaling). An important step of the approximation p...

This study presents a new finite element approximation for an optimal control problem (P ) governed by the heat equation and with end-point state constraints. The state constraint set S is assumed to have an empty interior in the state space. We begin with building a new penalty functional where the penalty parameter is an algebraic combination of the mesh size and the time step. Based on it, w...

objectives : this finite element method study aimed to compare the amount of stress on an isolated mandibular second premolar in two conventional reciprocal parallel interface designs of removable partial dentures (rpds) and the same rpd abutment tooth (not isolated). materials and methods: a kennedy class 1, modification 1 rpd framework was simulated on a 3d model of mandible with three differ...

in this study, an extended stress-based forming limit diagram (fld) for prediction of necking based on the marciniak and kucznski (m-k) model is represented and applied in tube hydroforming. the bulge forming of a straight tube is simulated by finite element method and verified with published experimental data. this adaptive simulation technique is based on the ability to detect the onset and g...

starting from two-dimensional (2d) equations of motion, discretized formulations for transient behavior of soil-structure interaction problems have been derived. two different dynamic infinite elements taking into account single and two-wave types are presented in transformed space. by coupling the infinite elements with standard finite elements, an ordinary finite element procedure is used for...

We study preconditioning techniques for discontinuous Galerkin discretizations of linear elasticity problems in primal (displacement) formulation. We propose a space splitting which gives rise to uniform preconditioners for the Interior Penalty (IP) Finite Element (FE) discretizations recently introduced in the works [12, 18, 19]. For the case when Dirichlet boundary conditions are imposed on t...