Finite element analysis of pressure formulation of the elastoacoustic problem

In this paper we analyze the non symmetric pressure/displacement formulation of the elastoacoustic vibration problem and show its equivalence with the (symmetric) stiffness coupling formulation. We introduce discretizations for these problems based on Lagrangian finite elements. We show that both formulations are also equivalent at discrete level and prove optimal error estimates for eigenfunctions and eigenvalues. Both formulations are rewritten such as to be solved with a standard Matlab eigensolver. We report numerical results comparing the efficiency of the methods over some test examples. Partially supported by Xunta de Galicia (Spain) through grant No. PGIDT00-PXI20701PR and by MCYT Research Project DPI2001-1613-C02-02Partially supported by Xunta de Galicia (Spain) through grant No. PGIDT00-PXI20701PR and by MCYT Research Project DPI2001-1613-C02-02Partially supported by FONDAP in Applied Mathematics (Chile) and by MCYT Research Projects DPI2001-1613-C02-02 and BFM2001-3261-C02-02Partially supported by FONDECYT (Chile) through grant No. 1.990.346 and FONDAP in Applied Mathematics (Chile)Mathematics Subject Classification (1991):65N30