Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
SIAM Journal on Numerical Analysis
Finite element approximation of a displacement formulation for time-domain elastoacoustic vibrations
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
SIAM Journal on Numerical Analysis
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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Two commonly used problem formulations for the description of acoustic wave propagation are investigated; one is based on fluid displacement, and the other one is based on the velocity potential as the primary variable. Their equivalence under general Neumann boundary conditions is shown on both the continuous and the discrete level. To obtain the equivalence in the discrete setting, a nonstandard mixed finite element formulation is introduced. Thus, the transfer of an already available analysis for coupled elasto-acoustic problems in the displacement formulation to the potential formulation can be achieved. For the applications, the potential formulation is of special interest because it allows the use of standard Lagrangian elements in both the stucture and the fluid subdomain. Moreover, the approach does not require any conformity of the subdomain meshes at the interface, which considerably simplifies the physics-adapted mesh generation. Several engineering examples demonstrate the applicability and efficiency of the resulting numerical scheme.