A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems, problems involving jumping coefficients, and finite element methods using anisotropic triangulations, such estimates often involve large factors, leading to sub-optimal error estimates. By making use of convex duality arguments, exact and explicit error representations are derived that avoid such effects.

翻译：后验误差估计是依赖可计算量来界定离散化误差的重要工具，其优势在于可避免建立常难以验证的正则性条件。针对非线性及不可微问题、含跳跃系数问题以及采用各向异性三角剖分的有限元方法，此类估计常包含较大因子，导致误差估计次优。通过引入凸对偶论证，本文推导出可规避此类效应的精确显式误差表示形式。