A Stable Space-Time Finite Element Method for Parabolic Evolution Problems

Abstract: This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on the FEM space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the FEM spaces yields an a priori discretization error estimate with respect to the discrete norm. Finally, we confirm the theoretical results with numerical experiments in spatial moving domains to confirm the theory presented.