Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions.Both simplicial and rectangular elements considered in two three dimensions.The based on P1, as conforming elements; however, it is necessary introduce new the case.Optimal order error estimates are demonstrated all cases with respect a broken norm H 1 (Ω) Robin L 2 (Ω).

A P1 -nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual nonconforming elements, which contain quadratic polynomials or of degree greater than 2, our consists only piecewise linear that are continuous at midpoints edges. One benefits using convenience rectangular meshes with least degrees freedom among elements. An optimal rate convergence obtained. Also a nonparametric reference scheme order to systematically...

Journal Article A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature Get access Dongwoo Sheen, Sheen Search other works by this author on: Oxford Academic Google Scholar Ian H. Sloan, Sloan Vidar Thomée IMA Numerical Analysis, Volume 23, Issue 2, April 2003, Pages 269–299, https://doi.org/10.1093/imanum/23.2.269 Published: 01 2003

We consider the inverse problem to refraction div$((1 + (k -1)\chi_D)\nabla u)=0 in $\Omega$ and $\pd{u}{\nu}=g$ on $\partial\Omega$. The is determine size location of an unknown object D from boundary measurement $\Lambda_D(g)=u|_{\bO}$. results this paper are twofold: stability estimation D. first obtain upper lower bounds by comparing $\Lambda_D(g)$ with Dirichlet data corresponding harmonic equation same Neumann g. then logarithmic case disks. In course deriving stability, we able...

We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using representation solution as integral along boundary sector in right half complex plane, then transforming this into real on finite interval $[0,1]$, and finally applying standard quadrature formula to integral. The method requires set elliptic problems with coefficients, which are independent may therefore be done parallel. is combined spatial elements.

A naturally parallelizable numerical method for approximating scalar waves in a single space variable is developed by going to frequency domain formulation. General forms of attenuation are permitted. Convergence established and results presented.

Abstract The objective of the present study is to show that numerical instability characterized by checkerboard patterns can be completely controlled when non‐conforming four‐node finite elements are employed. Since convergence element independent Lamé parameters, stiffness exhibits correct limiting behaviour, which desirable in prohibiting unwanted formation checkerboards topology optimization. We employ homogenization method checkerboard‐free property optimization problems and verify it...

A numerical method for approximating a pseudodifferential system describing attenuated, scalar waves is introduced and analyzed. Analytic properties of the solutions systems are determined used to show convergence method. Experiments using reported.

We present a nonconforming mixed finite element scheme for the approximate solution of time-harmonic Maxwell's equations in three-dimensional, bounded domain with absorbing boundary conditions on artificial boundaries. The numerical procedures are employed to solve direct problem magnetotellurics consisting determining scattered electromagnetic field model earth having conductivity anomalies arbitrary shapes. A domain-decomposition iterative algorithm which is naturally parallelizable and...

Let be given and suppose is an unknown object with known constant conductivity k. We consider the inverse problem of determining discontinuous coefficient from measurements electric voltage induced by current flux prescribed on . propose a general numerical algorithm for this implement to identify disc only one measurement.

As in the case of two-dimensional topology design optimization, numerical instability problems similar to formation checkerboard patterns occur if standard eight-node conforming brick element is used. Motivated by recent success non-conforming elements completely eliminating patterns, we aim at investigating performance three-dimensional controlling that are estimated overly stiff elements. To this end, will investigate how accurately estimate stiffness patterns. The estimation based on...

A parallel method for time discretization of backward parabolic problems is proposed. The problem reformulated to a set Helmholtz‐type with parameter on suitably chosen contour in the complex plane. After solving resulting elliptic equations, which can be solved parallel, we obtain regularized solution high frequency terms cut off by inverse Laplace transforms without requiring knowledge eigenfunctions differential operator. Since obtained artificial perturbation and components noise are...