A subdomain Galerkin/Least squares method for first-order elliptic systems in the plane
SIAM Journal on Numerical Analysis
Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
SIAM Journal on Numerical Analysis
Analysis and convergence of a covolume method for the generalized Stokes problem
Mathematics of Computation
Journal of Computational and Applied Mathematics
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
Analysis of the Cell Vertex Finite Volume Method for the Cauchy--Riemann Equations
SIAM Journal on Numerical Analysis
Covolume Solutions of Three-Dimensional Div-Curl Equations
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
A general mixed covolume framework for constructing conservative schemes for elliptic problems
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Analysis of a splitting method for incompressible inviscid rotational flow problems
Journal of Computational and Applied Mathematics
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In this paper we study continuous piecewise linear polynomial approximations to the generalized Stokes equations in the velocity-stress-pressure first-order system formulation by using a cell vertex finite volume/ least-squares scheme. This method is composed of a direct cell vertex finite volume discretization step and an algebraic least-squares step, where the least-squares procedure is applied after the discretization process is accomplished. This combined approach has the advantages of both finite volume and least-squares approaches. An error estimate in the H1 product norm for continuous piecewise linear approximating functions is derived. It is shown that, with respect to the order of approximation for H2-regular exact solutions, the method exhibits an optimal rate of convergence in the H1 norm for all unknowns, velocity, stress, and pressure.