Abstract
The mixed space-time finite element scheme for Sobolev equations was constructed through introduction of auxiliary variables. The scheme can not only reduce the order of the equation with the mixed method, but discretize both space and time variables by means of the finite element technique. A numerical model of high-order accuracy in space and time was obtained. The existence, stability and uniqueness of the mixed space-time finite element solution were proved. The error estimates were derived with the space-time projection operator.
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