A SPLIT LEAST-SQUARES CHARACTERISTIC MIXED ELEMENT METHOD FOR SOBOLEV EQUATIONS WITH A CONVECTION TERM
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초록
In this paper, we consider a split least-squares characteris- tic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term effi- ciently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares character- istic mixed element scheme for the given problem whose system is uncou- pled in the unknowns. We prove the optimal order in L2 and H1 normed spaces for the primal unknown and the suboptimal order in L2 normed space for the flux unknown.
Abstract
In this paper, we consider a split least-squares characteris- tic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term effi- ciently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares character- istic mixed element scheme for the given problem whose system is uncou- pled in the unknowns. We prove the optimal order in L2 and H1 normed spaces for the primal unknown and the suboptimal order in L2 normed space for the flux unknown.
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