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Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches

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Discontinuous mixed covolume methods for parabolic problems.

Ailing Zhu¹, Ziwen Jiang¹

¹School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China.

Thescientificworldjournal

|July 2, 2014

Summary

This summary is machine-generated.

We developed new discontinuous mixed covolume schemes for parabolic problems. These methods provide accurate solutions on triangular meshes, with proven error estimates for numerical analysis.

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Area of Science:

Numerical analysis
Computational mathematics
Partial differential equations

Background:

Parabolic problems are crucial in modeling various scientific phenomena.
Discretization methods are essential for solving these complex equations numerically.
Covolume methods offer a robust approach for spatial discretization.

Purpose of the Study:

To introduce novel semidiscrete and fully discrete discontinuous mixed covolume schemes.
To analyze the error bounds of these newly developed schemes.
To establish the accuracy and efficiency of the proposed numerical methods.

Main Methods:

Development of semidiscrete and backward Euler fully discrete discontinuous mixed covolume schemes.
Application of these schemes to parabolic problems on triangular meshes.
Rigorous error analysis to derive error estimates.

Main Results:

Optimal order error estimates were obtained in the discontinuous H(div) norm.
A first-order error estimate was achieved in the L(2) norm.
The schemes demonstrate effective performance for parabolic equations.

Conclusions:

The proposed discontinuous mixed covolume schemes are effective for parabolic problems.
The derived error estimates confirm the accuracy of the numerical methods.
These schemes offer a valuable tool for computational mathematics and scientific research.