Displaying similar documents to “Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes”

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 ...

The Influence of Look-Ahead on the Error Rate of Transcription

Y. R. Yamada, C. S. Peskin (2010)

Mathematical Modelling of Natural Phenomena

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In this paper we study the error rate of RNA synthesis in the look-ahead model for the random walk of RNA polymerase along DNA during transcription. The model’s central assumption is the existence of a in which ribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand before being hydrolyzed and linked covalently to the nascent RNA chain. An unknown, but important, integer parameter of this model is the window size...

Anisotropic mesh refinement in polyhedral domains: error estimates with data in L2(Ω)

Thomas Apel, Ariel L. Lombardi, Max Winkler (2014)

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

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The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the ()- and ()-norms by using a new quasi-interpolation...

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.

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...

Error Estimation for Reduced-Basis Approximation of Parametrized Elliptic Coercive Partial Differential Equations: “Convex Inverse” Bound Conditioners

Karen Veroy, Dimitrios V. Rovas, Anthony T. Patera (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equations with affine parameter dependence. The essential components are () (provably) rapidly convergent global reduced-basis approximations – Galerkin projection onto a space spanned by solutions of the governing partial differential equation at selected points in parameter space; () error estimation – relaxations of the error-residual...