The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation
provides a variational framework suitable for discretization using plane wave solutions
of an appropriate adjoint equation. Currently convergence of the method is only proved
on the boundary of the domain. However substantial computational evidence
exists showing that the method also converges throughout the domain of the Helmholtz equation. In this paper we exploit the fact that the UWVF is essentially an upwind discontinuous...
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent norm are derived.
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
We developed a mimetic finite difference method for solving elliptic equations
with tensor coefficients on polyhedral meshes. The first-order convergence
estimates in a mesh-dependent
norm are derived.
The paper deals with the application of a non-conforming domain
decomposition method
to the problem of the computation of induced currents in electric engines
with moving conductors.
The is considered as a quasi-static
approximation of Maxwell
equations and we study its two-dimensional formulation with either the
modified magnetic vector potential or the magnetic field as primary variable.
Two discretizations are proposed, the first one based on curved finite
elements
and the second one based...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
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