1,337 research outputs found
Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection
Polygonal finite elements generally do not pass the patch test as a result of
quadrature error in the evaluation of weak form integrals. In this work, we
examine the consequences of lack of polynomial consistency and show that it can
lead to a deterioration of convergence of the finite element solutions. We
propose a general remedy, inspired by techniques in the recent literature of
mimetic finite differences, for restoring consistency and thereby ensuring the
satisfaction of the patch test and recovering optimal rates of convergence. The
proposed approach, based on polynomial projections of the basis functions,
allows for the use of moderate number of integration points and brings the
computational cost of polygonal finite elements closer to that of the commonly
used linear triangles and bilinear quadrilaterals. Numerical studies of a
two-dimensional scalar diffusion problem accompany the theoretical
considerations
Moving-boundary problems solved by adaptive radial basis functions
The objective of this paper is to present an alternative approach to the conventional level set methods for solving two-dimensional moving-boundary problems known as the passive transport. Moving boundaries are associated with time-dependent problems and the position of the boundaries need to be determined as a function of time and space. The level set method has become an attractive design tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations. In the present approach, the moving interface is captured by the level set method at all time with the zero contour of a smooth function known as the level set function. A new approach is used to solve a convective transport equation for advancing the level set function in time. This new approach is based on the asymmetric meshless collocation method and the adaptive greedy algorithm for trial subspaces selection. Numerical simulations are performed to verify the accuracy and stability of the new numerical scheme which is then applied to simulate a bubble that is moving, stretching and circulating in an ambient flow to demonstrate the performance of the new meshless approach. (C) 2010 Elsevier Ltd. All rights reserved
Application of meshless methods to the analysis and design of grounding systems
4th World Congress on Computational Mechanics, 1998, Buenos Aires[Abstract] Analysis and design of grounding systems of electrical installations involves computing
the potential distribution in the earth and the equivalent resistance of the system.
Several numerical formulations based on the Boundary Element Method have recently
been derived for grounding grids embedded in uniform soils and in stratified soils,
which feasibility has been demonstrated with its application to large earthing systems in
a two-layer soil.
In cases of the analysis of grounding systems buried in more stratified soils or heterogeneous,
the application of Boundary Element approaches can require a considerable
computational effort. On the other hand, the specific geometry of earthing systems in
practice (a grid of interconnected buried conductors) precludes the use of standard numerical
techniques (such as finite elements or finite differences), since discretization
of the domain (the earth) is required and the obtention of suffciently accurate results
should imply unacceptable computing efforts.
For these reasons, we have turned our attention to investigate the applicability of numerical
formulations based on meshless methods for the grounding analysis. In this paper,
a meshless technique based on the Moving Least Square method with a point collocation
approach is proposed
The gradient discretisation method for linear advection problems
We adapt the Gradient Discretisation Method (GDM), originally designed for
elliptic and parabolic partial differential equations, to the case of a linear
scalar hyperbolic equations. This enables the simultaneous design and
convergence analysis of various numerical schemes, corresponding to the methods
known to be GDMs, such as finite elements (conforming or non-conforming,
standard or mass-lumped), finite volumes on rectangular or simplicial grids,
and other recent methods developed for general polytopal meshes. The scheme is
of centred type, with added linear or non-linear numerical diffusion. We
complement the convergence analysis with numerical tests based on the
mass-lumped P1 conforming and non conforming finite element and on the hybrid
finite volume method
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