On -manifolds and -surfaces for analysis of the convergence of mesh-based approximation.
Scully, Kevin (2005)
International Journal of Mathematics and Mathematical Sciences
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Scully, Kevin (2005)
International Journal of Mathematics and Mathematical Sciences
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Anita Hansbo, Peter Hansbo, Mats G. Larson (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
Marc Schweitzer (2012)
Open Mathematics
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This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical...
Qiding Zhu (1998)
Applications of Mathematics
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In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.
Nagata, Takashi (2010)
Journal of Applied Mathematics
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Faker Ben Belgacem, Padmanabhan Seshaiyer, Manil Suri (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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