A posteriori error estimation for the finite element method-of-lines solution of parabolic problems

Babuska and Yu constructed a posteriori estimates for finite element discre tization errors of linear elliptic problems utilizing a dichotomy principal stating that the errors of odd-order approximations arise near element edg es as mesh spacing decreases while those of even-order approximations arise in element interiors. We construct similar a posteriori estimates for the spatial errors of finite element method-of-lines solutions of linear parabo lic partial differential equations on square-element meshes. Error estimate s computed in this manner are proven to be asymptotically correct; thus, th ey converge in strain energy under mesh refinement at the same rate as the actual errors.