Characteristic-nonconforming finite-element methods for advection-dominated diffusion problems

AbstractIn this paper characteristic-nonconforming finite-element methods are studied for timedependent advection-dominated diffusion problems. The diffusion term in these problems is discretized using nonconforming finite elements, and the temporal differentiation and advection terms are treated by characteristic tracking schemes. Various nonconforming finite elements and characteristic tracking schemes are studied. Stability and convergence properties of the characteristic nonconforming methods are obtained; unconditionally stable results and error estimates of optimal order are established