Advances in Numerical Analysis and Approximation

Dear Colleagues,

The field of numerical analysis and approximation plays a pivotal role in the advancement of scientific computing and applied mathematics. It focuses on the development and analysis of algorithms for obtaining numerical solutions to complex mathematical problems, which are often intractable through analytical methods alone. This Special Issue aims to highlight the latest advancements in these crucial areas, with a particular emphasis on approximation techniques, integral equations, finite element methods (FEMs) and isogeometric analysis (IgA).

Approximation theory and finite element methods are foundational to numerous applications across science and engineering. For example, integral equations describe many problems in mathematical physics and mechanics or arise in the reformulation of boundary value problems.  Approximation techniques provide the tools to develop efficient methods for the numerical treatment of such equations and algorithms for estimating solutions to a wide range of other mathematical problems, while finite element methods are indispensable in solving partial differential equations (PDEs) that arise in various physical and engineering contexts. Furthermore, the new trend of isogeometric analysis (IgA) based on smooth splines combines FEMs with computer-aided designs, promoting high accuracy per degree of freedom. This makes IgA an interesting tool for solving PDEs.

We invite high-quality papers that present original research results and comprehensive review articles in the following areas:

• Approximation theory;
• Orthogonal polynomials;
• Numerical integration;
• Finite element methods (FEMs);
• Isogeometric analysis;
• Numerical treatment of integral equations;
• Numerical treatment of partial differential equations;
• Computational efficiency;
• Applications in science and engineering.

This Special Issue is dedicated to uncovering and promoting innovative research that advances the field of numerical analysis and approximation. We encourage submissions that not only contribute to the theoretical foundations, but also demonstrate practical applications and improvements in computational efficiency.

Dr. Federico Nudo
Dr. Domenico Mezzanotte
Dr. Salah Eddargani
Dr. Maria Carmela De Bonis
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• Polynomial approximation
• Orthogonal polynomials
• Integral equations
• Finite element methods (FEMs)
• Enriched finite element methods
• Approximation theory
• Isogeometric analysis
• Numerical analysis
• Numerical integration