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This paper first discusses the semilinear parabolic equation of Galerkin finite element method for time and space, using the finite element method and finite difference method combination of skills, proved the existence and uniqueness of weak solution, and are given respectively and time maximum modulus, space L ~ 2 die, namely L ~ ∞ (L ~ 2) die error estimation, and time maximum modulus, space H ~ 1 die error estimation. At the same time, the numerical example proved continuous space-time finite element method for semilinear parabolic equation of effectiveness. Secondly, discussed the semilinear parabolic integro-differential equation, using the nonlinear problem is transformed into equivalent linear problem skills, combined with continuous time and space finite element method gives linearization problem and the problem of error estimation.
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