This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of generalized special functions of bounded deformation which corresponds to the natural energy space for this functional. It is proved to be approximated in the sense of $Γ$-convergence by a sequence of discrete integral functionals defined on continuous piecewise affine functions. The main feature of this result is that the mesh is part of the unknown of the problem, and it gives enough flexibility to recover isotropic surface energies.
Adaptive Multiresolution Diffusion Operators: A Variational Theory on Evolving Multiresolution Spaces
King Fahd University of Petroleum and Minerals（阿卜杜拉国王科技大学）；Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway（挪威阿尔塔大学希莱拉斯量子分子科学中心化学系）；Algorithmiq S.r.l.（Algorithmiq有限公司）
Convergence and Optimality of Adaptive Mixed Finite Element Methods
University of California at Irvine（加州大学尔湾分校）；University of California at San Diego（加州大学圣地亚哥分校）；Peking University（北京大学）；Pennsylvania State University（宾夕法尼亚州立大学）
A correction adaptive two-grid finite element method for nonselfadjoint or indefinite elliptic problems
Lingnan Normal University（岭南师范学院）；Missouri University of Science and Technology（密苏里科技大学）；Guangzhou University（广州大学）；South China Normal University（华南师范大学）
Adaptive Multi-Grade Deep Learning for Highly Oscillatory Fredholm Integral Equations of the Second Kind
School of Computer Science and Engineering, Sun Yat-sen University（中山大学计算机科学与工程学院）；Department of Mathematics and Statistics, Old Dominion University（老道明大学数学与统计系）
Adaptively-refinable polar-spline discrete differential forms: hierarchical construction, exactness, and applications
Delft Institute of Applied Mathematics, Delft University of Technology（代尔夫特应用数学研究所，代尔夫特理工大学）；Department of Applied Mathematics, University of Santiago de Compostela（圣地亚哥德孔波斯特拉大学应用数学系）；Galician Centre for Mathematical Research and Technology (CITMAga), University of Santiago de Compostela（圣地亚哥德孔波斯特拉大学加利西亚数学研究与技术研究中心）
A C++ implementation of the discrete adjoint sensitivity analysis method for explicit adaptive Runge-Kutta methods enabled by automatic adjoint differentiation and SIMD vectorization
本文实现了一个面向自适应显式 Runge-Kutta 方法的 C++ 离散伴随灵敏度分析库，结合 AAD 与 SIMD 并行计算向量-Jacobian 乘积，性能略优于现有同类软件。
A priori error analysis for transient problems using Enhanced Velocity approach in the discrete-time setting
Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, University of Texas at Austin（德克萨斯大学奥斯汀分校地下建模中心计算工程与科学研究所）；School of Science and Technology, Nazarbayev University（纳扎尔巴耶夫大学理学院）
A Discrete Neural Operator with Adaptive Sampling for Surrogate Modeling of Parametric Transient Darcy Flows in Porous Media
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, Shandong Province, 266237, China（数学与交叉科学研究中心，山东大学，青岛，山东省，266237，中国）；Frontiers Science Center for Nonlinear Expectations, Minister of Education, Shandong University, Qingdao, Shandong Province, 266237, China（非线性期望前沿科学中心，教育部，山东大学，青岛，山东省，266237，中国）；School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong Province, 266580, China（石油工程学院，中国石油大学（华东），青岛，山东省，266580，中国）；Institute of Mathematical Sciences, ShanghaiTech University, Pudong, Shanghai, 201210, China（数学科学研究院，上海科技大学，浦东，上海，201210，中国）；School of Civil Engineering, Qingdao University of Technology, Qingdao, Shandong Province, 266520, China（土木工程学院，青岛科技大学，青岛，山东省，266520，中国）
