A least-squares spectral finite element method was used to develop an accurate computer code for prediction of solidification from a melt under the influence of an externally applied magnetic field. The computational results indicate significantly different flow-field patterns and thermal fields in the melt and the accrued solid in the cases of full gravity, reduced gravity, and an applied unif...

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of KohnSham density-functional theory (DFT). To this end, we develop an a priori mesh adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy ...

It is well known that the classic Galerkin finite element method is unstable when applied to hyperbolic conservation laws such as the Euler equations for compressible flow. It is also well known that naively adding artificial diffusion to the equations stabilizes the method but sacrifices too much accuracy to be of any practical use. An elegant approach, referred to as spectral viscosity method...

Standard spectral methods are capable of providing very accurate approximations to well-behaved smooth functions with significantly less degrees of freedom when compared with finite difference or finite element methods (cf. [6,7,11]). However, if a function exhibits localized behaviors such as sharp interfaces, very thin internal or boundary layers, using a standard Gauss-type grid usually fail...

In this work we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the Fokker–Planck equation and some similar equations. ...

In this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting, alternating direction or, more generally, fractional step methods. Such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive Runge–Kutta method, which is called the fractional step Runge–Kutta met...

Abstract. We analyse the spectral bounds of non-overlapping domain decomposition additive Schwarz preconditioners for hp-version discontinuous Galerkin finite element methods in H-type norms. Using original approximation results for discontinuous finite element spaces, it is found that these preconditioners yield a condition number bound of order 1 + Hp/hq, where H and h are respectively the co...