Moving finite element, least squares, and finite volume approximations of steady and time-dependent PDEs in multidimensions
نویسندگان
چکیده
منابع مشابه
Least-squares Finite Element Approximations to Solutions of Interface Problems∗
A least-squares finite element method for second-order elliptic boundary value problems having interfaces due to discontinuous media properties is proposed and analyzed. Both Dirichlet and Neumann boundary data are treated. The boundary value problems are recast into a firstorder formulation to which a suitable least-squares principle is applied. Among the advantages of the method are that nonc...
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1Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, IN 47907-1395, USA. Email: [email protected]. 2Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA. Email: [email protected]. 3MAB, CNRS UPRESA 5466, Université de Bordeaux I, 351 Cours de la Libération, 33400 Takence, France. Email: hzhang@m...
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For multivariate problems with many scattered data locations the use of radial functions has proven to be advantageous. However, using the usual radial basis function approach one needs to solve a large (possibly dense) linear system. In the moving least squares (MLS) method one obtains a best approximation of the given data in a (moving) weighted least-squares sense. The computational burden i...
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Least-squares finite element methods are an attractive class of methods for the numerical solution of partial differential equations. They are motivated by the desire to recover, in general settings, the advantageous features of Rayleigh–Ritz methods such as the avoidance of discrete compatibility conditions and the production of symmetric and positive definite discrete systems. The methods are...
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We consider the application of least-squares variational principles to the numerical solution of partial differential equations. Our main focus is on the development of least-squares finite element methods for elliptic boundary value problems arising in fields such as fluid flows, linear elasticity, and convection-diffusion. For many of these problems, least-squares principles offer numerous th...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00519-7