Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

Finite element methods (FEM) continue to be a cornerstone of computational science, offering robust strategies for the numerical solution of partial differential equations, including those governing ...

This is a preview. Log in through your library . Abstract A stochastic collocation method for solving linear parabolic partial differential equations with random coefficients, forcing terms, and ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

The members of the group Geometric Analysis and Partial Differential Equations have broad interests in analysis and geometry. Active research topics include quasiconformal analysis and partial ...