Abstract
Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of finite element analysis.
Highlights
Consider the following initial-boundary value problem of pseudo-hyperbolic equation f X,t, in 0,T, u X, t0, on 0,T, (1)On the other hand, H1-Galerkin mixed finite element method has been under rapid progress recently since this method has the following advantages over classical mixed finite element method
Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes
The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of finite element analysis
Summary
H1-Galerkin mixed finite element method (see [4]) has been under rapid progress recently since this method has the following advantages over. Shi and Wang [8] investigated this method for integro-differential equation of parabolic type with nonconforming finite elements including the ones studied in [9,10] It is well-known that the convergence behavior of the well-known nonconforming Wilson element is much better than that of conforming bilinear element. [19,20,21,22,23,24] generalized the results mentioned above and constructed a class of Quasi-Wilson elements which are convergent to the second order elliptic problem for narrow quadrilateral meshes [23]. We will focus on H1-Galerkin nonconforming mixed finite element approximation to problem (1) under arbitrary quadrilateral meshes. The corresponding optimal order error estimates are obtained for semi-discrete scheme
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