The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always correctly...

The problem of modeling acoustic waves scattered by an object with
Neumann boundary condition is considered. The boundary condition is
taken into account by means of the fictitious domain method, yielding
a first order in time mixed variational formulation for the
problem. The resulting system is discretized
with two families of mixed finite elements that are compatible with
mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always...

In error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup
stability constants is essential. In [Huynh ,
(2007) 473–478], the authors presented an efficient
method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to
minimizing a linear functional under a few linear constraints. These constraints depend on nested sets of parameters...

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