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A multi-space error estimation approach for meshfree methods

Rüter, Marcus, Chen, Jiun-Shyan (2015)

Application of Mathematics 2015

Error-controlled adaptive meshfree methods are presented for both global error measures, such as the energy norm, and goal-oriented error measures in terms of quantities of interest. The meshfree method chosen in this paper is the reproducing kernel particle method (RKPM), since it is based on a Galerkin scheme and therefore allows extensions of quality control approaches as already developed for the finite element method. Our approach of goal-oriented error estimation is based on the well-established...

A note on n-ary Poisson brackets

Michor, Peter W., Vaisman, Izu (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

An n -ary Poisson bracket (or generalized Poisson bracket) on the manifold M is a skew-symmetric n -linear bracket { , ⋯ , } of functions which is a derivation in each argument and satisfies the generalized Jacobi identity of order n , i.e., ∑ σ ∈ S 2 n - 1 ( sign σ ) { { f σ 1 , ⋯ , f σ n } , f σ n + 1 , ⋯ , f σ 2 n - 1 } = 0 , S 2 n ...

A note on necessary and sufficient conditions for convergence of the finite element method

Kučera, Václav (2015)

Application of Mathematics 2015

In this short note, we present several ideas and observations concerning finite element convergence and the role of the maximum angle condition. Based on previous work, we formulate a hypothesis concerning a necessary condition for O ( h ) convergence and show a simple relation to classical problems in measure theory and differential geometry which could lead to new insights in the area.

A note on tension spline

Segeth, Karel (2015)

Application of Mathematics 2015

Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the results of...

A parallel method for population balance equations based on the method of characteristics

Li, Yu, Lin, Qun, Xie, Hehu (2013)

Applications of Mathematics 2013

In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher dimensional population balance equation into a series of lower dimensional convection-diffusion-reaction equations which can be solved in a parallel way. Some numerical results are presented to show the accuracy and efficiency.

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