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作者:Huangxin Chen , Shuyu Sun
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.136 (3), pp.805-839
摘要:In this paper we develop an a posteriori error estimator for a mixed finite element method for single-phase Darcy flow in a two-dimensional fractured porous media. The discrete fracture model is applied to model the fractures by one-dimensional fractures in a two-dimensional...
作者:D. Gallistl , P. Huber , D. Peterseim
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.137 (2), pp.339-351
摘要:This paper studies global stability properties of the Rayleigh–Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios \(\hat{\lambda }_k/\lambda _k\) of the k th numerical eigenvalue \(\hat{\lambda }_k\) and the k th exact eigenvalue \(\lambd...
作者:A. Abdulle , M. E. Huber
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.136 (3), pp.603-649
摘要:We introduce a numerical homogenization method based on a discontinuous Galerkin finite element heterogeneous multiscale method to efficiently approximate the effective solution of parabolic advection–diffusion problems with rapidly varying coefficients, large Péclet number ...
作者:Carsten Carstensen , Eun-Jae Park , Philipp Bringmann
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.136 (4), pp.1097-1115
摘要:The first-order div least squares finite element methods provide inherent a posteriori error estimator by the elementwise evaluation of the functional. In this paper we prove Q -linear convergence of the associated adaptive mesh-refining strategy for a sufficiently fine initial m...
作者:Andrea Cangiani , Emmanuil H. Georgoulis , Tristan Pryer ...
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.137 (4), pp.857-893
摘要:An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on q...
作者:Hoang Tran , Clayton G. Webster , Guannan Zhang
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.137 (2), pp.451-493
摘要:In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized elliptic PDEs with finite-dimensional deterministic and stochastic inputs. Such methods construct an o...
作者:Peter Oswald
来源:[J].Applications of Mathematics(IF 0.222), 2017, Vol.62 (5), pp.433-457
摘要:Compared to conforming P1 finite elements, nonconforming P1 finite element discretizations are thought to be less sensitive to the appearance of distorted triangulations. E.g., optimal-order discrete H 1 norm best approximation error estimates for H 2 functi...
作者:Yaozong Tang , Xiaolin Li
来源:[J].Applications of Mathematics(IF 0.222), 2017, Vol.62 (5), pp.477-492
摘要:The meshless element-free Galerkin method is developed for numerical analysis of hyperbolic initial-boundary value problems. In this method, only scattered nodes are required in the domain. Computational formulae of the method are analyzed in detail. Error estimates and convergen...
作者:Yunzhang Zhang , Chao Xu , Jiaquan Zhou
来源:[J].Boundary Value Problems(IF 0.922), 2017, Vol.2017 (1)
摘要:The stability and convergence of a linearly extrapolated second order backward difference (BDF2-LE) time-stepping scheme for solving viscoelastic fluid flow in \(\mathbb{R}^{d}\) , \(d=2,3\) , are presented in this paper. The time discretization is based on the implicit sche...

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