International Journal of Differential Equations and Applications

In this paper we construct and analyze a variational algorithm forapproximating nonlinear parabolic partial differential equations with anonlinear boundary condition. The algorithm consists of approximating thesolution by a linear scheme based on Rothe's method to discrete with respectto time. The numerical solution converges strongly in the space $C((0,T)$; $%L_{2}(\Omega ))\cap L_{2}((0,T)$;$W^{1,\;2}(\Omega ))$. Moreover, the errorestimate of the solution is also derived.