Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions

Long Chen; Xuehai Huang

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arXiv · 1611.03936

Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions

Long Chen·Xuehai Huang

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Abstract

A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes and Helmholtz decompositions in a general way. Discretizing the decoupled formulation leads to a natural superconvergence between the Galerkin projection and the decoupled approximation. Examples include but not limit to: the primal formulations and mixed formulations of biharmonic equation, fourth order curl equation, and triharmonic equation etc. As a by-product, Helmholtz decompositions for many dual spaces are obtained.

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Long Chen, Xuehai Huang. 2016-11-12. Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions. https://arxiv.org/abs/1611.03936

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