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
Carsten Carstensen, Petr Plecháč (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. error estimates motivate an adaptive mesh-refining algorithm for efficient discretization....
Marco Picasso, Jacques Rappaz (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and error estimates are established using a Newton-chord fixed point theorem, error estimates are also derived. An...
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...
J. R. Fernández, D. Santamarina (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an error...