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：后验误差估计是一种重要工具，可通过可计算量来界定离散化误差，同时避免通常难以建立的正则性条件。对于非线性不可微问题、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系数，导致误差估计结果非最优。通过运用凸对偶论证，本文推导出精确且显式的误差表示形式，从而避免此类效应。