Domain decomposition modified with characteristic mixed finite element of compressible oil-water seepage displacement and its numerical analysis

A parallel algorithm, structured by domain decomposition and characteristic mixed finite element, is presented for solving three-dimensional displacement problem of compressible seepage flow. Decomposing the computational domain into several subdomains, we define a characteristic function to approximate the value on interior boundary at previous time level and obtain numerical solutions implicitly in subdomains in parallel. The flow equation is treated by the method of mixed finite element and the saturation equation is approximated by the method of characteristic finite element. For a model problem we apply variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, the theory and technique of priori estimates of differential equations to derive optimal error estimate in l2 norm. Numerical data are consistent with theoretical analysis and show that this method is effective in solving actual applications. Then it can solve the well-known problem.