Analysis of multiscale mortar mixed approximation of nonlinear elliptic equations

Muhammad Arshad, Eun-Jae Park, Dong wook Shin

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A multiscale mortar mixed finite element method is established to approximate non-linear second order elliptic equations. The method is based on non-overlapping domain decomposition and mortar finite element methods. The existence and uniqueness of the approximation are demonstrated, and a priori L2-error estimates for the velocity and pressure are derived. An error bound for mortar pressure is proved. Convergence estimates of the mortar pressure are based on a linear interface formulation having the discrete-pressure dependent coefficient. Optimal order convergence is achieved on the fine scale by a proper choice of mortar space and polynomial degree of approximation. The quadratic convergence of the Newton–Raphson method is proved for the nonlinear algebraic system arising from the mortar mixed formulation of the problem. Numerical experiments are performed to support theoretic results.

Original languageEnglish
Pages (from-to)401-418
Number of pages18
JournalComputers and Mathematics with Applications
Volume75
Issue number2
DOIs
Publication statusPublished - 2018 Jan 15

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Mortar
Nonlinear Elliptic Equations
Mortar Finite Element Method
Approximation
Nonoverlapping Domain Decomposition
Degree of Approximation
Convergence Estimates
Second Order Elliptic Equations
Mixed Formulation
Convergence Order
Quadratic Convergence
Newton-Raphson
Mixed Finite Element Method
Error Bounds
Finite element method
Error Estimates
Existence and Uniqueness
Numerical Experiment
Polynomial
Formulation

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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Analysis of multiscale mortar mixed approximation of nonlinear elliptic equations. / Arshad, Muhammad; Park, Eun-Jae; Shin, Dong wook.

In: Computers and Mathematics with Applications, Vol. 75, No. 2, 15.01.2018, p. 401-418.

Research output: Contribution to journalArticle

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