Improved error estimation of dynamic finite element methods for second-order parabolic equations

Dynamic finite element schemes are analyzed for second-order parabolic problems. These schemes permit different finite element spaces at different time levels in order to efficiently capture time-changing localized phenomena, such as moving sharp fronts or layers. The dynamical change of grids and interpolation polynomials is necessary and essential to many large-scale transient problems. Standard, characteristic, and mixed finite element methods with dynamic function spaces are considered for linear and nonlinear problems in a unified framework with improved a priori error estimates and convergence results.