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An adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems
 Math. Comp
"... An ecient and reliable a posteriori error estimate is derived for linear parabolic equations which does not depend on any regularity assumption on the underlying elliptic operator. An adaptive algorithm with variable timestep sizes and space meshes is proposed and studied which, at each time step, ..."
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Cited by 27 (1 self)
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An ecient and reliable a posteriori error estimate is derived for linear parabolic equations which does not depend on any regularity assumption on the underlying elliptic operator. An adaptive algorithm with variable timestep sizes and space meshes is proposed and studied which, at each time step
Adaptive finite element algorithms for the Stokes problem: Convergence rates and optimal computational complexity
, 2006
"... Abstract. Although adaptive finite element methods (FEMs) are recognized as powerful techniques for solving mixed variational problems of fluid mechanics, usually they are not even proven to converge. Only recently, in [SINUM, 40 (2002), pp.12071229] Bänsch, Morin and Nochetto introduced an adaptiv ..."
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Cited by 3 (1 self)
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Uzawa finite element algorithm that uses a generalization of the optimal adaptive FEM of Stevenson [SINUM, 42 (2005), pp.21882217] as an inner solver. By adding a derefinement step to the resulting adaptive Uzawa algorithm, in order to optimize the underlying triangulation after each fixed number
Molecular Based Mathematical Biology Research Article • DOI: 10.2478/mlbmb20130005 • MBMB • 2012 • 90108 Parallel Adaptive Finite Element Algorithms for Solving the Coupled Electrodiffusion Equations
"... In this paper we present parallel adaptive finite element algorithms for solving the 3D electrodiffusion equations such as the PoissonNernstPlanck equations and the sizemodified PoissonNernstPlanck equations in simulations of biomolecular systems in ionic liquid. A set of transformation meth ..."
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In this paper we present parallel adaptive finite element algorithms for solving the 3D electrodiffusion equations such as the PoissonNernstPlanck equations and the sizemodified PoissonNernstPlanck equations in simulations of biomolecular systems in ionic liquid. A set of transformation
Automatic verification of finitestate concurrent systems using temporal logic specifications
 ACM Transactions on Programming Languages and Systems
, 1986
"... We give an efficient procedure for verifying that a finitestate concurrent system meets a specification expressed in a (propositional, branchingtime) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent ..."
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Cited by 1388 (62 self)
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We give an efficient procedure for verifying that a finitestate concurrent system meets a specification expressed in a (propositional, branchingtime) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent
A tutorial on particle filters for online nonlinear/nonGaussian Bayesian tracking
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2002
"... Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and nonGaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data online as it arrives, both from the point of view o ..."
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Cited by 2006 (2 self)
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of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/nonGaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass
A rapid hierarchical radiosity algorithm
 Computer Graphics
, 1991
"... This paper presents a rapid hierarchical radiosity algorithm for illuminating scenes containing lar e polygonal patches. The afgorithm constructs a hierarchic“J representation of the form factor matrix by adaptively subdividing patches into su bpatches according to a usersupplied error bound. The a ..."
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Cited by 409 (11 self)
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This paper presents a rapid hierarchical radiosity algorithm for illuminating scenes containing lar e polygonal patches. The afgorithm constructs a hierarchic“J representation of the form factor matrix by adaptively subdividing patches into su bpatches according to a usersupplied error bound
unknown title
, 2014
"... An anisotropic adaptive finite element algorithm for transonic viscous flows around a wing ..."
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An anisotropic adaptive finite element algorithm for transonic viscous flows around a wing
Convergence of a simple adaptive finite element method for . . .
, 2007
"... We prove convergence and optimal complexity of an adaptive finite element algorithm for a model problem of optimal control. Following previous work, our algorithm is based on an adaptive marking strategy which compares a simple edge estimator with an oscillation term in each step of the algorithm i ..."
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Cited by 2 (1 self)
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We prove convergence and optimal complexity of an adaptive finite element algorithm for a model problem of optimal control. Following previous work, our algorithm is based on an adaptive marking strategy which compares a simple edge estimator with an oscillation term in each step of the algorithm
A Posteriori Error Analysis And Adaptivity For Finite Element Approximations Of Hyperbolic Problems
, 1997
"... this article is to present an overview of recent developments in the area of a posteriori error estimation for finite element approximations of hyperbolic problems. The approach pursued here rests on the systematic use of hyperbolic duality arguments. We also discuss the question of computational ..."
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Cited by 25 (4 self)
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of computational implementation of the a posteriori error bounds into adaptive finite element algorithms
A Multiscale Finite Element Method For Elliptic Problems In Composite Materials And Porous Media
 JOURNAL OF COMPUTATIONAL PHYSICS
, 1997
"... In this paper, we study a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales. The method is designed to efficiently capture the large scale behavior of the solution without resolving ..."
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Cited by 312 (27 self)
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resolving all the small scale features. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator. Our method is applicable to general multiplescale problems without restrictive assumptions. The construction
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