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20201029 馮新龍 A layers capturing type H-adaptive FEM for convection-diffusion-reaction equations on surfaces

發布時間:2020-10-28 15:05    瀏覽次數:    來源:

題目:A layers capturing type H-adaptive FEM for convection-diffusion-reaction equations on surfaces
摘要:In this work, we study the FE approximation of surface convection-diffusion-reaction equations which are important fundamental model problems in simulations of complex physical phenomena on moving interfaces, ultra-thin materials and biological films. The optimal error estimates of FEM are shown. According to the analyze results, the solutions of convection-dominated diffusion problems have low accuracy in the regions of layers. To overcome such drawback which may lead to non-physical oscillations, the adaptive mesh refinement method is considered. Due to the numerical characteristic of non-physical oscillations and layers, we present an error estimator which specializes in capturing the non-physical oscillations and layers. The mesh refinement marking strategies which take into account the large curvatures of the surfaces are developed. The proposed method can efficiently capture layers, non-physical oscillations and provide high resolution solutions with fewer degree of freedoms. A series of numerical examples are designed to demonstrate the effectiveness of the proposed H-adaptive method and make exploration of the solution behavior of convection-dominated diffusion problems on surfaces.
報告人簡介:馮新龍,現為新疆大學數學與系統科學學院教授, 博士生導師。主要研究科學計算、不確定性量化、計算流體力學、圖像處理與數據分析、保險精算等。發表學術論文160余篇,其中SCI 140篇。2020年“熱耦合流體模型的高效高精度保物理性質算法研究”獲自治區科學技術進步獎一等獎【自然科學獎】?,F擔任中國精算師、中國數學會理事?,F主持一個科研計劃項目、一個面上項目、一個重點項目。

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