CAJ | 학술논문

针对结构自适应加密网格（ SAMR）上扩散方程的求解，分析几种有限体格式的逼近性，同时设计和分析一种两层网格算法。首先，讨论一种常见的守恒型有限体格式，并给出网格加密区域和细化/粗化插值算子的条件；接着，通过在粗细界面附近引入辅助三角形单元，消除粗细界面处的非协调单元，设计了一种保对称有限体元（ SFVE）格式，分析表明，该格式具有更好的逼近性，且对网格加密区域和插值算子的限制更弱；最后，为SFVE格式构造一种两层网格（ TL）算法，理论分析和数值实验表明该算法的一致收敛性。
침대결구자괄응가밀망격（ SAMR）상확산방정적구해，분석궤충유한체격식적핍근성，동시설계화분석일충량층망격산법。수선，토론일충상견적수항형유한체격식，병급출망격가밀구역화세화/조화삽치산자적조건；접착，통과재조세계면부근인입보조삼각형단원，소제조세계면처적비협조단원，설계료일충보대칭유한체원（ SFVE）격식，분석표명，해격식구유경호적핍근성，차대망격가밀구역화삽치산자적한제경약；최후，위SFVE격식구조일충량층망격（ TL）산법，이론분석화수치실험표명해산법적일치수렴성。
We analyze approximation and propose a two-level algorithm for finite volume schemes of diffusion equations with structured adaptive mesh refinement. First of all, a typically conservative finite volume scheme was discussed, along with criterion for refining and coarsening interpolation operator. Secondly, non-conforming elements around coarse-fine interface were eliminated by introducing auxiliary triangle elements. A symmetric finite volume element ( SFVE) scheme was designed. And further analysis showed the scheme has better approximation. It weakens restrictions. Finally, a two-level algorithm was constructed for SFVE. Theoretical analysis and numerical experiments demonstrate uniform convergence of the algorithm.