Least-squares Mixed Finite Element Methods For Two Kinds Of Partial Differential Equations

Least-squares mixed finite element method is proposed for hyperbolic integro-differential equations and the technique of combining the least-squares mixed finite element method and the characteristic method are discussed for Sobolev equation. The advantage of Least-squares mixed finite element method is that it is not subject to LBB condition,so we can select the finite element spaces more flexibly. Characteristic method permits the use of large time teps,and avoids or sharply reduces the usual numerical difficulties.Least-squares mixed finite element method is used to solve hyperbolic integro-differential equations.The convergence analysis are also given.A new least-squares mixed finite element method is studied for the Sobolev equations. The finite element scheme is given,and the convergence analysis shows that the method yields the approximate solutions with accuracy optimal.The technique of combining the least-squares mixed finite element method and the characteristic method are used to propose the finite element scheme for convection-dominated Sobolev equation. The proofs of error estimates are also given.