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High accuracy analysis of a new nonconforming mixed finite element scheme for Sobolev equations. (English) Zbl 1244.65143
The authors consider an initial-boundary value problem attached to a 2D linear Sobolev type equation. First, they rewrite the problem in a mixed form as a system of lower-order PDEs. Then, they are concerned with a nonconforming finite element approximation of the spatial derivatives coupled with a backward Euler approximation of the time derivative. They claim high accuracy. However, the estimations reported in Theorems 2 and 3 do not seem to be proper for unbounded solutions as is the case with the solution of the numerical example carried out. Their right hand side of these estimations contain integrals with respect to time of the norms of the time derivatives of the exact solution beside the contribution of the initial data.
MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
35Q35PDEs in connection with fluid mechanics
65M12Stability and convergence of numerical methods (IVP of PDE)
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