The convergence of Rothe's method for parabolic differential equations
The convergence of the full discretization scheme (time discretized Galerkin method is proved for the nonlinear evolution equation \[ u_ t(x,t)+\sum_{| i| \leq m}(-1)^{| i|}D^ iA_ i(x,t,Du)=f(x,t) \] with Dirichlet boundary conditions under monotonicity and coerciveness assumptions on A(x,t,s) in s and polynomial growth conditions. The corresponding system of algebraic equations is nonlinear. The convergence is obtained in the space \(L_{\infty}(0,T;L_ 2(\Omega))\).
scientific article; zbMATH DE number 4115892