Two unconditional stable schemes for simulation of heat equation on manifold using DEC

TL;DR

This paper introduces two new unconditional stable numerical schemes based on discrete differential calculus for simulating heat diffusion on manifolds, ensuring stability and accuracy through maximum principle analysis.

Contribution

The paper presents novel unconditional stable schemes for heat equation simulation on manifolds using discrete differential calculus, with proven stability and error bounds.

Findings

Schemes are unconditionally stable.

Error analysis confirms accuracy.

Applicable to heat diffusion on manifolds.

Abstract

To predict the heat diffusion in a given region over time, it is often necessary to find the numerical solution for heat equation. With the techniques of discrete differential calculus, we propose two unconditional stable numerical schemes for simulation heat equation on space manifold and time. The analysis of their stability and error is accomplished by the use of maximum principle.