Dynamic Finite Element Methods for Second Order Parabolic Equations

Dynamic nite element schemes are analyzed for second order parabolic problems. These schemes can employ di erent nite element spaces at di erent time levels in order to capture time-changing localized phenomena, such as moving sharp fronts or layers. The dynamically changing grids and interpolation polynomials are necessary and essential to many large-scale transient problems. Standard, characteristic, and mixed nite element methods with dynamic function spaces are considered for linear and nonlinear problems. The convergence results obtained in this paper are optimal and better than those published previously.