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Recently, Hofreither, Langer and Pechstein have analyzed a nonstandard finite element method based on element-local boundary integral operators. The method is able to treat general polyhedral meshes and employs locally PDE-harmonic trial functions. In the previous work, the primal formulation of...
We study in this paper a P1 finite element approximation of the solution in of a biharmonic problem. Since the P1 finite element method only leads to an approximate solution in , a discrete Laplace operator is used in the numerical scheme. The convergence of the method is shown, for the general...
We give a theorem on error estimates of approximate solutions for the ordinary functional differential equation. The error is estimated by a solution of an initial problem for nonlinear differential functional equation. We apply this general result to the investigation of the convergence of the...
We discuss numerical properties of continuous Galerkin––Petrov and discontinuous Galerkin time discretizations applied to the heat equation as a prototypical example for scalar parabolic partial differential equations. For the space discretization, we use biquadratic quadrilateral finite...
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