The research challenges in numerical methods in engineering are in constant evolution. The two driving forces for this evolution are the development of novel methods and algorithms and the investigation of new fields of application where numerical modelling opens unexplored perspectives to experimentalists and practitioners. We took occasion of Prof. Antonio Huerta's sixtieth birthday to ponder the current trends of the discipline, the questions to be answered in the near future and the most promising lines of work. Antonio's research record is essentially transversal, covering many different topics and applications in the broad fields of mathematical and computational modelling and computational engineering. Distilling his work in the last decade and his perspectives in the years to come, we identified the keywords forming the title of this special issue of the International Journal for Numerical Methods in Engineering: credibility, high‐fidelity, and reduced computational cost.

In fact, simulations in daily industrial practice are characterised by computationally demanding problems for which fast, accurate, and reliable numerical strategies are required. Thus, with a large variety of problems spanning, for example, from aerodynamics to solid mechanics, from vibro‐acoustics to thermo‐mechanics and microfluidics, the three keywords (credibility, high‐fidelity, and reduced computational cost) are common features in modern computational engineering techniques.

The concept of credibility in computational engineering pertains to the technologies allowing to assess and control the accuracy of the computed numerical approximations and the uncertainty of models and data, including error estimation and uncertainty quantification. The high‐fidelity paradigm requires the employment of advanced discretisation techniques, for example, high‐order methods, to capture complex features of the phenomena under analysis, in close connection with credibility tools. Of course, the computational cost of these procedures may represent a bottleneck for their application to realistic problems. In this context, low‐cost methodologies, including lowest‐order discretisations, reduced order models as well as mesh, degree, and model adaptivity play a crucial role to make computational engineering methods and algorithms affordable.

The 12 manuscripts in this special issue cover a wide range of techniques related to the above mentioned topics, including: accurate high‐order1, 2 and fast lowest‐order discontinuous Galerkin discretisations;3, 4 mesh,1-3, 5 degree,1 and modal basis6, 7 adaptivity; a priori error estimates,8 a posteriori error indicators,1, 3 error bounds,5, 7, 9, 10 and error estimates in quantities of interest;2, 6, 9, 10 a priori5, 10, 11 and a posteriori2, 6-9, 12 reduced order models.

The papers included in this special issue are a representative sample of insights in state‐of‐the‐art technologies and innovative ideas in computational engineering that will contribute to keep the interest of the scientific community in the disciplines covered by the International Journal for Numerical Methods in Engineering.

工程数值方法的研究挑战不断发展。这种发展的两个驱动力是新方法和算法的发展以及对新应用领域的研究，其中数值建模为实验家和实践者开辟了未探索的视角。我们借着安东尼奥·韦尔塔（Antonio Huerta）教授六十岁生日的机会，思考该学科的当前趋势，在不久的将来要回答的问题以及最有前途的工作。Antonio的研究记录基本上是横向的，涵盖了数学和计算建模以及计算工程等广泛领域中的许多不同主题和应用。提炼过去十年的工作和未来几年的观点，信誉，高保真度并降低了计算成本。

实际上，在日常工业实践中，模拟的特征是计算要求很高的问题，因此需要快速，准确和可靠的数值策略。因此，在从空气动力学到固体力学，从振动声学到热力学和微流体学等各种各样的问题中，三个关键词（信誉，高保真度和降低的计算成本）是现代的共同特征。计算工程技术。

计算工程中的可信度概念属于允许评估和控制所计算的数值近似值的准确性以及模型和数据的不确定性（包括误差估计和不确定性量化）的技术。该高保真范式需要的先进技术，离散化的就业，例如，高阶方法，捕捉到的现象，复杂的特点分析下，与信誉工具紧密结合。当然，这些过程的计算成本可能表示将其应用于实际问题的瓶颈。在这种情况下，低成本方法论包括最低阶离散化，降阶模型以及网格，度和模型适应性，对于使计算工程方法和算法可负担得起至关重要的作用。

本期特刊中的12篇论文涵盖了与上述主题相关的多种技术，包括：准确的高阶1、2和快速的最低阶非连续Galerkin离散化；3、4目，1-3、5度，1和模态基础6、7适应性；先验的误差估计，8个 后验误差指示符，1,3误差界，5，7，9，10点在感兴趣的量和误差估计; 2，6，9，10 先验5，10，11和后验2，6-9，12降阶模型。

本期特刊中的论文是代表性的最新技术见解和计算工程创新思想的样本，这将有助于保持科学界对《国际数值方法杂志》所涵盖学科的兴趣工程学。