These lecture notes for a graduate course present an introduction to the mathematical theory of finite element methods for the numerical solution of partial differential equations. Covered are conforming and nonconforming (in particular, discontinuous Galerkin and mixed methods) for elliptic partial differential equations and Galerkin methods for parabolic equations.
A multi-modes Monte Carlo finite element method for elliptic partial differential equations with random coefficients
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations
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