Publicación: DISCONTINUOUS GALERKIN METHODS FOR THE ACOUSTIC VIBRATION PROBLEM
Fecha
2023
Título de la revista
ISSN de la revista
Título del volumen
Editor
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Resumen
IN TWO AND THREE DIMENSION WE ANALYZE DISCONTINUOUS GALERKIN METHODS (DG) FOR THE ACOUSTIC VIBRATION PROBLEM. THROUGH ALL OUR STUDY WE CONSIDER AN INVISCID FLUID, LEADING TO A LINEAR EIGENVALUE PROBLEM. THE ACOUSTIC PROBLEM IS WRITTEN, IN FIRST PLACE, IN TERMS OF THE DISPLACEMENT. UNDER THE APPROACH OF THE NON-COMPACT OPERATORS THEORY, WE PROVE CONVERGENCE AND ERROR ESTIMATES FOR THE METHOD WHEN THE DISPLACEMENT FORMULATION IS CONSIDERED. WE ANALYZE THE INFLUENCE OF THE STABILIZATION PARAMETER ON THE COMPUTATION OF THE SPECTRUM, WHERE SPURIOUS
EIGENMODES ARISE WHEN THIS PARAMETER IS NOT CORRECTLY CHOSEN. ALTERNATIVELY WE PRESENT THE
FORMULATION DEPENDING ONLY ON THE PRESSURE, COMPARING THE PERFORMANCE OF THE DG METHODS
WITH THE PURE DISPLACEMENT FORMULATION. COMPUTATIONALLY, WE STUDY THE INFLUENCE OF THE
STABILIZATION PARAMETER ON THE ARISING OF SPURIOUS EIGENVALUES WHEN THE SPECTRUM IS COMPUTED.
ALSO, WE REPORT TESTS IN TWO AND THREE DIMENSIONS WHERE CONVERGENCE RATES ARE REPORTED,
TOGETHER WITH A COMPARISON BETWEEN THE DISPLACEMENT AND PRESSURE FORMULATIONS FOR THE
PROPOSED DG METHODS.
Descripción
Palabras clave
Galerkin method, Error estimates, Eigenvalue problems, Discontinuous
