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Discrete reliability for high-order Crouzeix--Raviart finite elements

1. 연구 배경 및 동기 비정합 FEM인 Crouzeix–Raviart 요소는 경계조건을 완화하면서도 높은 차수 다항식으로 확장 가능하다는 장점이 있다. 그러나 차수가 높아질수록 비정합 공간이 메시 정제 시에 비중첩(non‑nested) 이 되는 문제가 발생한다. 이는 적응형 알고리즘의 이론적 수렴 분석, 특히 “적응성 공리” 중 이산 신뢰성(A3) 을 증명하는 데 큰 장애물이다. 기존 연구는 주로 CR( 1) (최저 차수) 에 한정되어 있었으며, 고차수에 대한 일반적인 이론은 부재했다. 2. 핵심 기여 새로운 국소 준보간 연산

Discrete reliability for high-order Crouzeix--Raviart finite elements

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