Numerical methods for partial differential equations

Partial differential equations are ubiquitous in many domains of sciences and industry, as they model phenomena with spatial and temporal variations. Most of these models are too complex to be exactly solved, and numerical methods are the only way to gather quantitative behaviour on the solutions. This unit covers the design, analysis and implementation of numerical methods for partial differential equations. Topics covered can include finite difference methods, finite element methods, finite volume methods, error analysis, elliptic equations, parabolic equations, implementation in dynamic languages (such as Python or Julia). The focus will be on the design of the methods, their mathematical analysis, and their implementation and numerical testing.