ABSTRACT:
Wave equations model many important applications, such as acoustics and oceanic tides. Mixed finite element methods discretize the conservative first-order form of such equations and preserve important mathematical and physical structure. I will begin by surveying some of the basic features of these discretizations. Then, I will present new semi discrete energy estimates for linear tide models. These estimates give long-term stability and, in the absence of forcing terms, give exponential decay of solution profiles to a steady, solenoidal field. However, these results still leave important practical details related to algorithms and software open, such as time-stepping and enabling the right kinds of operations efficiently. I will conclude by surveying some of the challenges that thus presented to software tools such as FEniCS and Firedrake.
ADDITIONAL INFORMATION: