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- Hansbo, Peter F G, 1959, et al.
(author)
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Piecewise divergence free discontinuous Galerkin methods
- 2008
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In: Communications in Numerical Methods in Engineering. - : Wiley. - 1069-8299 .- 1099-0887. ; 24:5, s. 355-366
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Journal article (peer-reviewed)abstract
- In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix-Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions.
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- Bengzon, Fredrik, 1978-, et al.
(author)
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Adaptive piecewise constant discontinuous Galerkin methods for convection-diffusion problems
- 2009
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Other publication (other academic/artistic)abstract
- In this paper we present a discontinuous Galerkin method with piecewise constant approximation for convection-diffusion type equations. We show that if the discretization is carefully chosen, then the method is optimal in the L2 norm as well as in a discrete energy norm measuring the normal flux across element boundaries. We also derive a posteriori error estimates and illustrate their effectiveness in combination with adaptive mesh refinement on a few benchmark problems.
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- Bengzon, Fredrik, 1978-, et al.
(author)
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Simulation of multiphysics problems using adaptive finite elements
- 2006
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In: Applied parallel computing state of the art in scientific computing. - umeå : department of Mathematics, Umeå University. ; , s. 1-14
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Conference paper (peer-reviewed)abstract
- Real world applications often involve several types of physics. In practice, one often solves such multiphysics problems by using already existing single physics solvers. To satisfy an overall accuracy, it is critical to understand how accurate the individual single physics solution must be. In this paper we present a framework for a posteriori error estimation of multiphysics problems and derive an algorithm for estimating the total error. We illustrate the technique by solving a coupled flow and transport problem with application in porous media flow.
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