Smooth complex geological surface reconstruction based on partial differential equations

Yao, Xiangjuan; Deng, Shi-Wu; Liu, Zhining; Hu, Guangmin; Jia, Yu; Chen, Xiaoer; Wen, Zongguo

doi:10.1190/segam2015-5898238.1

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“…In geophysics, sixth-order PDE are used to overcome difficulties involving complex geological faults [35]. Indeed, sixth-order PDE arise in a variety of geophysical contexts due to their appearance as models in electromagneto-thermoelasticity [30] and relation to equatorial electrojets [34].…”

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A mixed finite element method for a sixth-order elliptic problem

Droniou

Ilyas

Lamichhane

et al. 2017

IMA Journal of Numerical Analysis

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We consider a saddle-point formulation for a sixth-order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to formulate our saddle-point problem and the finite element method. The new formulation allows us to use the H 1 -conforming Lagrange finite element spaces to approximate the solution. We prove A priori error estimates for our approach. Numerical results are presented for linear and quadratic finite element methods.Key words. sixth-order problem, higher order partial differential equations, biharmonic problem, mixed finite elements, error estimates.

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confidence: 99%