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
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.
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...
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...
Irene Kyza (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ 75 (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...
Irene Kyza (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ...
Sacha Krug (2013)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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The traveling salesman problem (TSP) is one of the most fundamental optimization problems. We consider the -metric traveling salesman problem ( -TSP), , the TSP restricted to graphs satisfying the -triangle inequality ({}) ≤ (({}) + ({})), for some cost function and any three vertices . The well-known path matching Christofides algorithm (PMCA) guarantees an approximation ratio of 3 /2 and is the best known algorithm for the -TSP, for 1 ≤ ≤ 2....