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Abstract This paper considers a singularly perturbed reaction diffusion problem. It is investigated whether adaptive approaches are successful to design robust solution procedures. A key ingredient is the a posteriori error estimator. Since robust and mathematically analysed error estimation is possible in the energy norm, the focus is on this choice of norm and its implications. The numerical performance...
The h-h/2-strategy is one well-known technique for the a posteriori error estimation for Galerkin discretizations of energy minimization problems. One considers $${\eta:=\Vert\phi_{h/2}-\phi_h\Vert}$$ to estimate the error $${\Vert\phi-\phi_h\Vert}$$ , where $${\phi_h}$$ is a Galerkin solution with respect to a mesh $${\mathcal{T}_h}$$ and $${\phi_{h/2}}$$ is a Galerkin solution...
The discontinuous Galerkin method in time for the coupling of conforming finite element and boundary element methods was established in Part I of this paper, where quasi-optimal a priori error estimates are provided. In the second part, we establish a posteriori error estimates and so justify an adaptive space/time-mesh refinement algorithm for the efficient numerical treatment of the time-dependent...
The h-h/2-strategy is one well-known technique for the a posteriori error estimation for Galerkin discretizations of energy minimization problems. One considers $${\eta:=\Vert\phi_{h/2}-\phi_h\Vert}$$ to estimate the error $${\Vert\phi-\phi_h\Vert}$$ , where $${\phi_h}$$ is a Galerkin solution with respect to a mesh $${\mathcal{T}_h}$$ and $${\phi_{h/2}}$$ is a Galerkin solution with respect to the...
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