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703
Infsup testing of upwind methods
, 2000
"... We propose inf–sup testing for finite element methods with upwinding used to solve convection–diffusion problems. The testing evaluates the stability of a method and compactly displays the numerical behaviour as the convection effects increase. Four discretization schemes are considered: the standar ..."
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Cited by 7 (5 self)
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We propose inf–sup testing for finite element methods with upwinding used to solve convection–diffusion problems. The testing evaluates the stability of a method and compactly displays the numerical behaviour as the convection effects increase. Four discretization schemes are considered
Multidimensional upwind methods for hyperbolic conservation laws
 J. Comput. Phys
, 1990
"... We present a class of secondorder conservative finite difference algorithms for solving numerically timedependent problems for hyperbolic conservation laws in several space variables. These methods are upwind and multidimensional, in that the numerical fluxes are obtained by solving the characteri ..."
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Cited by 145 (25 self)
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We present a class of secondorder conservative finite difference algorithms for solving numerically timedependent problems for hyperbolic conservation laws in several space variables. These methods are upwind and multidimensional, in that the numerical fluxes are obtained by solving
Ordered Upwind Methods for Static HamiltonJacobi Equations: Theory and Algorithms
, 2003
"... We develop a family of fast methods for approximating the solutions to a wide class of static Hamilton–Jacobi PDEs; these fast methods include both semiLagrangian and fully Eulerian versions. Numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear ..."
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Cited by 136 (9 self)
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discretized equations. Our techniques, which we refer to as “Ordered Upwind Methods” (OUMs), use partial information about the characteristic directions to decouple these nonlinear systems, greatly reducing the computational labor. Our techniques are considered in the context of controltheoretic and front
ConstraintPreserving Upwind Methods for Multidimensional Advection Equations
"... A general framework for constructing constraintpreserving numerical methods is presented and applied to a multidimensional divergenceconstrained advection equation. This equation is part of a set of hyperbolic equations that evolve a vector field while locally preserving either its divergence or c ..."
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Cited by 11 (2 self)
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methods that preserve exactly the discretized constraint by special flux distribution. Assuming a rectangular, twodimensional grid as a first approach, application of this framework leads to a locally constraintpreserving multidimensional upwind method. We prove consistency and stability of the new
A HIGHERORDER UPWIND METHOD FOR VISCOELASTIC FLOW
"... We present a conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two dimensions. We model the incompressible Navier–Stokes equations with an extra viscoelastic stress described by the OldroydB constitutive equations. The equations are cast in ..."
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We present a conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two dimensions. We model the incompressible Navier–Stokes equations with an extra viscoelastic stress described by the OldroydB constitutive equations. The equations are cast
Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle ” Phenomenon
, 1999
"... Some upwind formulations promote severe instabilities that originate in the numerical capturing of shocks; this is known as the “carbuncle ” phenomenon. An analysis of the linearized form of the algorithms is carried out to explain and predict the generation of such instabilities. The information ..."
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obtained is then used to design remedies that only slightly and locally modify the original schemes. c ° 2001 Academic Press Key Words: fluid dynamics; shock waves; upwind methods; numerical instability; “carbuncle ” phenomenon.
Fast Marching and Ordered Upwind Methods as applied to Robot Motion Planning
"... Fast Marching and Ordered Upwind Methods are numerical approximation techniques for describing the propagation of a curve in time. These methods are special cases of the Level Set Methods introduced by J.A. Sethian. To get a basic idea of what these methods describe, think of a shock wave moving out ..."
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Fast Marching and Ordered Upwind Methods are numerical approximation techniques for describing the propagation of a curve in time. These methods are special cases of the Level Set Methods introduced by J.A. Sethian. To get a basic idea of what these methods describe, think of a shock wave moving
On CFL Evolution Strategies for Implicit Upwind Methods in Linearized Euler Equations ∗
, 2006
"... In implicit upwind methods for the solution of linearized Euler equations, one of the key issues is to balance large time steps, leading to a fast convergence behavior, and small time steps, needed to sufficiently resolve relevant flow features. A time step is determined by choosing a CourantFriedr ..."
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In implicit upwind methods for the solution of linearized Euler equations, one of the key issues is to balance large time steps, leading to a fast convergence behavior, and small time steps, needed to sufficiently resolve relevant flow features. A time step is determined by choosing a Courant
Dijkstralike ordered upwind methods for solving static HamiltonJacobi equations
, 2010
"... The solution of a static HamiltonJacobi Partial Differential Equation (HJ PDE) can be used to determine the change of shape in a surface for etching/deposition/lithography applications, to provide the firstarrival time of a wavefront emanating from a source for seismic applications, or to compute ..."
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Cited by 3 (1 self)
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stencil which are smaller. This causal property is related but not the same thing as an upwinding property of schemes for time dependent problems. The solution to such a discretized system of equations can be efficiently computed using a Dijkstralike method in a single pass through the grid nodes
Results 1  10
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703