The finite element method (FEM) has evolved into a robust and flexible tool for solving partial differential equations (PDEs) defined on surfaces. Its versatility allows for the treatment of ...

The honor, like a Nobel Prize for mathematics, was given this year to Luis Caffarelli for his work on partial differential equations. By Kenneth Chang As a mathematician, Luis A. Caffarelli of the ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really ...

Now researchers have built new kinds of artificial neural networks that can approximate solutions to partial differential equations orders of magnitude faster than traditional PDE solvers. And once ...

Many dynamic processes can be described mathematically with the aid of stochastic partial differential equations. Scientists have found a new method which helps to solve a certain class of such ...

Waveguide-based structures can solve partial differential equations by mimicking elements in standard electronic circuits. This novel approach, developed by researchers at Newcastle University in the ...

Based at the University of Texas at Austin, Caffarelli started work on partial differential equations (PDEs) in the late 1970s and has contributed to hundreds of papers since.

Partial differential equations are generally solved by breaking complex shapes like airplane wings or body organs into grids or meshes made of small elements. The problem is then solved on each ...