CutFEM based on extended finite element spaces

Abstract We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation partial differential equations. In methods so called cut elements intersected by the boundary occur these must in stabilized some way. Discrete provides such stabilization modification space close boundary. More, precisely is extended from stable interior over way which also guarantees optimal properties. Our applicable all standard nodal based various order regularity. an abstract theory elliptic problems associated parabolic time dependent equations derive priori error estimates. finally apply this examples different including interface problems, biharmonic operator sixth triharmonic operator.