A Stable Space-Time Finite Element Method for Parabolic Evolution Problems
Provides a theoretically grounded numerical method for parabolic evolution problems on moving domains, but the contribution is incremental as it extends existing space-time FEM concepts.
The paper introduces a new stable space-time finite element method for parabolic problems on moving domains, proving ellipticity and a priori error estimates, with numerical validation.
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.