NDLI: Ultraconvergence of high order FEMs for elliptic problems with variable coefficients

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Numerische Mathematik : Volume 136, Issue 2, June 2017

Numerische Mathematik : Volume 136, Issue 1, May 2017

A linear finite volume method for nonlinear cross-diffusion systems

Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement

Legendre spectral collocation in space and time for PDEs

Boundary integral formulation and semi-implicit scheme coupling for modeling cells under electrical stimulation

Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations

Randomized estimation of spectral densities of large matrices made accurate

Ultraconvergence of high order FEMs for elliptic problems with variable coefficients

Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects

The stability of extended Floater–Hormann interpolants

On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit II. Analytic regularity

Numerische Mathematik : Volume 135

Numerische Mathematik : Volume 134

Numerische Mathematik : Volume 133

Numerische Mathematik : Volume 89

Ultraconvergence of high order FEMs for elliptic problems with variable coefficients

Content Provider	Springer Nature Link
Author	He, Wen ming Zhang, Zhimin Zou, Qingsong
Copyright Year	2016
Abstract	In this paper, we investigate local ultraconvergence properties of the high-order finite element method (FEM) for second order elliptic problems with variable coefficients. Under suitable regularity and mesh conditions, we show that at an interior vertex, which is away from the boundary with a fixed distance, the gradient of the post-precessed kth $$(k\ge 2)$$ order finite element solution converges to the gradient of the exact solution with order $$\mathcal{O}(h^{k+2} (\mathrm{ln} h)^3)$$ . The proof of this ultraconvergence property depends on a new interpolating operator, some new estimates for the discrete Green’s function, a symmetry theory derived in [26], and the Richardson extrapolation technique in [20]. Numerical experiments are performed to demonstrate our theoretical findings.
Ending Page	248
Page Count	34
Starting Page	215
File Format	PDF
ISSN	0029599X
e-ISSN	09453245
Journal	Numerische Mathematik
Issue Number	1
Volume Number	136
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-08-22
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	ApplicationMathematics/Computational Methods of Engineering Mathematical Methods in Physics Eigenvalue problems Numerical Analysis Theoretical, Mathematical and Computational Physics Error bounds Mathematics Numerical and Computational Physics, Simulation Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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Ultraconvergence of high order FEMs for elliptic problems with variable coefficients

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