Generalized Lax equivalence theory for the compressible Navier-Stokes system

Abstract 

In this talk we discuss a generalized Lax equivalence theory for the compressible Navier-Stokes system: convergence = stability + consistency. First, we introduce the concept of consistent approximation representing the (energy/entropy) stability and consistency of suitable numerical solutions. Then, by passing to the limit we obtain a dissipative weak solution with the only information derived from the stability of the consistent approximation. Further, we show that the dissipative weak solution coincide with the strong solution as long as the latter exists. Consequently, any numerical solution belonging to the class of consistent approximation convergences to the strong solution. Finally, we present a numerical example.

About the speaker 

佘邦伟，毕业德国美茵茨大学，曾任捷克科学院数学所准聘、长聘研究员，现为首都师范大学研究员，主要研究方向为流体力学方程组的数值分析和模拟，在Numer. Math.、IMA J Numer. Anal.、SIAM J Numer. Anal.、Math. Comput.、J Comput. Phys.、Multi. Model Simul.等计算数学领域的知名期刊发表多篇学术论文，著有Springer专著一部。