2017
DOI: 10.1002/num.22163
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A postprocessed flux conserving finite element solution

Abstract: We propose a local postprocessing method to get a new finite element solution whose flux is conservative element‐wise. First, we use the so‐called polynomial preserving recovery (postprocessing) technique to obtain a higher order flux which is continuous across the element boundary. Then, we use special bubble functions, which have a nonzero flux only on one face‐edge or face‐triangle of each element, to correct the finite element solution element by element, guided by the above super‐convergent flux and the e… Show more

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Cited by 3 publications
(3 citation statements)
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“…In fact, although certain numerical methods can be devised specifically to satisfy some conservation laws [e.g., finite volume methods conserve flux [46], symplectic ordinary differential equation (ODE) integrators conserve energy [47]), most numerical methods (including standard FEM formulations) do not satisfy physical invariants exactly. For instance, Zhang et al [48] discussed what modifications of the FEM are necessary to render it flux conserving. As part of this work, we will investigate how well the NNM satisfies physical invariants of the slit-well problem in the absence of any problem-specific customization.…”
Section: Physical Realism Of Nnm Solutionsmentioning
confidence: 99%
“…In fact, although certain numerical methods can be devised specifically to satisfy some conservation laws [e.g., finite volume methods conserve flux [46], symplectic ordinary differential equation (ODE) integrators conserve energy [47]), most numerical methods (including standard FEM formulations) do not satisfy physical invariants exactly. For instance, Zhang et al [48] discussed what modifications of the FEM are necessary to render it flux conserving. As part of this work, we will investigate how well the NNM satisfies physical invariants of the slit-well problem in the absence of any problem-specific customization.…”
Section: Physical Realism Of Nnm Solutionsmentioning
confidence: 99%
“…We define an interpolation operator. Because of the non-local frame functions (x−v i ) α , similar situations happened also in [5,6,9,[14][15][16][17][18], the interpolation operator cannot be local (I h u| K depends on u| K only), but quasi-local, i.e. (I h u)| K depends on u| ω K , where ω K is the union of elements which touch a vertex of K. On a mesh T h , we select sequentially but randomly some free elements (none of its vertices is a vertex of a selected element) until no more such an element, see Fig.…”
Section: The Convergence Theorymentioning
confidence: 79%
“…This method employs a low-order mixed finite element formulation based on least-squares formalism by enforcing explicit constraints of various type. In [48], the authors develop elementwisely-conservative flux also by post-processing the FEM solution element-by-element. Their method is valid for any order schemes and their post-processed solution converges with optimal order both in H 1 and L 2 norms.…”
mentioning
confidence: 99%