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This thesis aims at investigating the first steps toward an unconditionallystable space-time isogeometric method, based on splines of maximal regularity,for the linear acoustic wave equation. The unconditional stability ofspace-time discretizations for wave propagation problems is a topic ofsignificant interest, by virtue of the advantages of space-time methodscompared with more standard time-stepping techniques. In the case of continuousfinite element methods, several stabilizations have been proposed. Inspired byone of these works, we address the stability issue by studying the isogeometricmethod for an ordinary differential equation closely related to the waveequation. As a result, we provide a stabilized isogeometric method whoseeffectiveness is supported by numerical tests. Motivated by these results, weconclude by suggesting an extension of this stabilization tool to thespace-time isogeometric formulation of the acoustic wave equation.

Stability of space-time isogeometric methods for wave propagation problems