Abstract
Sobolev equation appears in many areas of physics. The study about sobolev equations has important significance for solving physical engineering problems. With the sobolev equations we can analyze the flow of fluids through fissured rock, and obtain the process of the migration of the moisture in soil and solve thermodynamics problems, etc. There have been many numerical modeling methods for sobolev equations, such as difference methods and finite element methods. A mixed finite element method was established and the error estimate was carried out in [1], and a characteristics mixed finite element method was given in [2]. The collocation methods that meet constraint condition of interpolation have been developed since the 1970s. The methods satisfy the differential equation and the boundary conditions at collocation points by the piecewise polynomial approximation. Because the collocation method is easy to get approximation equations, does not need to compute numerical integration and has high-order accuracy, it is widely used in mathematical physics and engineering problems. For example, the collocation method in quasilinear parabolic equations was used in [3]. The collocation method in heat conduction equations was considered in [4]. Consider the linear sobolev equation with constant coefficients
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