Refining the Galerkin method error estimation for parabolic type problem with a boundary condition

The article considers a parabolic-type boundary value problem with divergent principal part, when the condition contains time derivative of required function: { u t − d/dx i ( x,t,u, ∇ )+ )=0, 0 + )cos( v,x )= g ),( x,t )∈ S , x,0 x ), ∈ Ω Such nonclassical problems conditions containing desired function arise in study number applied problems, for example, surface body, whose temperature is same at all its points, washed off by well-mixed liquid, or homogeneous isotropic body placed inductor an induction furnace and electro-magnetic wave falls on surface. have been little studied, therefore, parabolic type, function, relevant. In this paper, definition generalized solution considered space H ˜1,1 Q T ) given. This solved approximate Bubnov-Galerkin method. coordinate system chosen from 1 (Ω). To determine coefficients solution, reduced to ordinary differential equations. aim obtain under which estimate error norm (Ω) has order O h k −1 paper first explores auxiliary elliptic problem. When ellipticity satisfied, inequalities are proposed difference Using these estimates, as well additional included consideration, estimates method function.