کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4645180 | 1632197 | 2014 | 17 صفحه PDF | دانلود رایگان |
A variational inequality (VI) and a mixed formulation for an elliptic obstacle problem are considered. Both formulations are discretized by an hp -FE interior penalty discontinuous Galerkin (IPDG) method. In the case of the mixed method, the discrete Lagrange multiplier is a linear combination of biorthogonal basis functions. In particular, also the discrete problems are equivalent. For these formulations a residual based a posteriori error estimate and a hierarchical a posteriori error estimate are derived. For the mixed method the residual based estimate is constructed explicitly, for which the approximation error is split into a discretization error of a linear variational equality problem and additional consistency and obstacle condition terms. For the VI-method a hierarchical estimate based on an overkill solution is derived explicitly. This includes the h–h/2h–h/2 and p–(p+1)p–(p+1)-estimates. The numerical experiments show exponential convergence up to the desired tolerance.
Journal: Applied Numerical Mathematics - Volume 76, February 2014, Pages 76–92