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2015•Advances in computer science researchOpen access

Numerical Algorithm of Two Mixed Finite Element Schemes for A Fourth-Order Diffusion Equation

Jinfeng Wang, Hong Li, Yang Liu

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Abstract

Two numerical algorithms based on H 1 -Galerkin mixed finite element (GMFE) methods are presented and analyzed for a fourth-order diffusion equation.By introducing three variables with two different ways, the two first-order system of four equations are formulated.The semi-discrete optimal error estimates are derived for a numerical scheme and the fully discrete analysis of optimal error results for the other one are made.Moreover, the numerical procedures for two numerical schemes are made to confirm the theoretical results of theorems.

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Two numerical algorithms based on H 1 -Galerkin mixed finite element (GMFE) methods are presented and analyzed for a fourth-order diffusion equation.By introducing three variables with two different ways, the two first-order system of four equations are formulated.The semi-discrete optimal error estimates are derived for a numerical scheme and the fully discrete analysis of optimal error results for the other one are made.Moreover, the numerical procedures for two numerical schemes are made to confirm the theoretical results of theorems.

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Available abstract

Two numerical algorithms based on H 1 -Galerkin mixed finite element (GMFE) methods are presented and analyzed for a fourth-order diffusion equation.By introducing three variables with two different ways, the two first-order system of four equations are formulated.The semi-discrete optimal error estimates are derived for a numerical scheme and the fully discrete analysis of optimal error results for the other one are made.Moreover, the numerical procedures for two numerical schemes are made to confirm the theoretical results of theorems.

Key concepts: Finite element method, Order (exchange), Computer science, Algorithm, Diffusion, Applied mathematics, Diffusion equation, Mixed finite element method

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