Displaying similar documents to “Anisotropic mesh refinement in polyhedral domains: error estimates with data in L2(Ω)”

Optimal convergence rates of mortar finite element methods for second-order elliptic problems

Faker Ben Belgacem, Padmanabhan Seshaiyer, Manil Suri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present an improved, near-optimal error estimate for a non-conforming finite element method, called the mortar method (M0). We also present a new mortaring technique, called the mortar method (MP), and derive , and error estimates for it, in the presence of quasiuniform and non-quasiuniform meshes. Our theoretical results, augmented by the computational evidence we present, show that like (M0), (MP) is also a viable mortaring technique for the method.

Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes

A. Agouzal, K. Lipnikov, Yu. Vassilevsk (2010)

Mathematical Modelling of Natural Phenomena

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We present a new method for generating a -dimensional simplicial mesh that minimizes the -norm, > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method

Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions

A. Agouzal, N. Debit (2010)

Mathematical Modelling of Natural Phenomena

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Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain of , ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative ...

Error Control and Andaptivity for a Phase Relaxation Model

Zhiming Chen, Ricardo H. Nochetto, Alfred Schmidt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The phase relaxation model is a diffuse interface model with small parameter which consists of a parabolic PDE for temperature and an ODE with double obstacles for phase variable . To decouple the system a semi-explicit Euler method with variable step-size is used for time discretization, which requires the stability constraint . Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter are further employed for space discretization. error estimates...

A piecewise P2-nonconforming quadrilateral finite element

Imbunm Kim, Zhongxuan Luo, Zhaoliang Meng, Hyun NAM, Chunjae Park, Dongwoo Sheen (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce a piecewise -nonconforming quadrilateral finite element. First, we decompose a convex quadrilateral into the union of four triangles divided by its diagonals. Then the finite element space is defined by the set of all piecewise -polynomials that are quadratic in each triangle and continuously differentiable on the quadrilateral. The degrees of freedom (DOFs) are defined by the eight values at the two Gauss points on each of the four edges...