First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Least-squares mixed finite elements for second-order elliptic problems
SIAM Journal on Numerical Analysis
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
SIAM Journal on Numerical Analysis
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A remark on least-squares mixed element methods for reaction-diffusion problems
Journal of Computational and Applied Mathematics
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In this paper, a split least-squares characteristic mixed finite element method for a kind of Sobolev equation with convection term is proposed, in which the characteristic method is based on the approximation of the material derivative term, that is, the time derivative term plus the convection term. The resulting least-squares procedure can be split into two independent symmetric positive definite sub-schemes and does not need to solve a coupled system of equations. Theory analysis shows that the method yields the approximate solutions with optimal accuracy in L^2(@W) norm for the primal unknown and in H(div;@W) norm for the unknown flux, respectively. Numerical examples in one dimension, which are consistent with the theoretical results, are provided to demonstrate the characteristic behavior of this approach.