DOLFINx is the next generation problem solving environment from the FEniCS Project; it provides an expressive and performant framework for solving partial differential equations using the finite element method. Designed for parallelism from the ground up, DOLFINx supports arbitrary-degree finite elements on a wide range of (possibly curved) cell shapes across the full de Rham complex, as well as user-defined custom elements. It preserves the high level of mathematical abstraction associated with the FEniCS project, while enabling extensibility and fine-grained customization via user-defined element kernels and direct access to low-level data structures. At its core, DOLFINx adopts a modern, data-oriented and functional-inspired design and avoids the deep class hierarchies typical of more traditional finite element libraries. This approach yields a compact, maintainable, and flexible library that enables the development of high-performance programs in different languages and which enables efficient integration with other widely used numerical libraries and tools.

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