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This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes.
A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the other schemes...
We propose and analyze several finite-element schemes for solving a grade-two
fluid model, with a
tangential boundary condition, in a two-dimensional polygon. The exact
problem is split into a
generalized Stokes problem and a transport equation, in such a way that it
always has a solution
without restriction on the shape of the domain and on the size of the data.
The first scheme uses
divergence-free discrete velocities and a centered discretization of the
transport term, whereas the
other schemes...
In this work we consider the dual-primal Discontinuous Petrov–Galerkin (DPG) method for the advection-diffusion model problem. Since in the DPG method both mixed internal variables are discontinuous, a static condensation procedure can be carried out, leading to a single-field nonconforming discretization scheme. For this latter formulation, we propose a flux-upwind stabilization technique to deal with the advection-dominated case. The resulting scheme is conservative and satisfies a discrete maximum...
In this work we consider the
dual-primal Discontinuous Petrov–Galerkin (DPG)
method for the advection-diffusion model problem.
Since in the DPG method both
mixed internal variables are discontinuous,
a static condensation procedure can be
carried out, leading to a single-field nonconforming
discretization scheme. For this latter formulation,
we propose a flux-upwind stabilization technique to deal with
the advection-dominated case.
The resulting scheme is conservative and satisfies a discrete...
We propose and analyse a abstract framework for augmented mixed formulations.
We give a priori error estimate in the general case: conforming and
nonconforming approximations with or without numerical integration.
Finally, a posteriori error estimator is given. An example of stabilized
formulation for Stokes problem is analysed.
There is a growing interest in high-order finite and spectral/hp element
methods using continuous and discontinuous Galerkin formulations. In this paper we
investigate the effect of h- and p-type refinement on
the relationship between runtime performance and solution accuracy. The broad spectrum of
possible domain discretisations makes establishing a performance-optimal selection
non-trivial. Through comparing the runtime of different implementations...
We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants...
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