On measures of errors for nonlinear variational problems

摘要

We consider a class of convex variational problems and deduce computable and unconditional upper bounds of quantities, which are certain measures of errors associated with an approximation. Also, we discuss closely related mathematical questions, which are important for the a posteriori error estimation theory of nonlinear problems. Namely, we present generalized forms of the Prager-Synge estimate and of the Mikhlin's variational identity, a generalized form of the Helmholtz decomposition theorem, and derive a general estimate of the distance to the set equilibrated fields.