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A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King...
We are concerned with a finite element approximation for time-harmonic wave
propagation governed by the Helmholtz equation. The usually oscillatory behavior of
solutions, along with numerical dispersion, render standard finite element methods
grossly inefficient already in medium-frequency regimes. As an alternative, methods
that incorporate information about the solution in the form of plane waves have
been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that
...
In this paper, we study a postprocessing procedure for improving
accuracy of the finite volume element approximations of semilinear
parabolic problems. The procedure amounts to solve a source problem
on a coarser grid and then solve a linear elliptic problem on a
finer grid after the time evolution is finished. We derive error
estimates in the L2 and H1 norms for the standard finite
volume element scheme and an improved error estimate in the H1
norm. Numerical results demonstrate the accuracy...
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