[PDE & Applications seminar] Vanja Nikolic: Asymptotic-preserving analysis and finite element discretizationin nonlinear acoustics

09 maart 2023 16:00 t/m 17:00 - Locatie: Snijderszaal LB 01.010 EEMCS | Zet in mijn agenda

Research in nonlinear acoustics is fueled by a growing number of high-intensity ultrasound applications in medicine and industry. At high intensities or frequencies, sound evolution is quasilinear, and in tissue like-media, additionally nonlocal effects of time-fractional type come into play. This application field gives rise to many interesting mathematical questions involving nonlinear and nonlocalacoustic equations, such asdealing with their singular behavior in the vanishing limit ofcertain medium parameters. In this talk, we will present some of our recent work on the robust mathematical and numerical analysis of singularly perturbed nonlinearand nonlocal acoustic wave equations. We will focus on the analysis of conforming finite element discretizations in space in the latter context andwave equations of Westervelt-type with (non)local dissipation. Here we will draw parallels from their uniform treatment in the continuous setting, as both rest upon devising appropriate energy functionals that remain stable in the zero dissipationlimit.