#### Academic department under which the project should be listed

CSM - Mathematics

#### Research Mentor Name

Yuliya Babenko

#### Abstract (300 words maximum)

Laplace’s equation is a partial differential equation of the second order, which has a different use in mathematical physics (electrostatistics, mechanics, thermodynamics, etc.). Frequently also boundary condition is added (Dirichlet’s problem). The solution to this problem is well known. Our goal in this study is to develop an optimal method of recovery of the solution based on information we have on hand about the function (the function is not fully known. For example is known at N equally spaced points) and to compute the optimal error between the actual solution and the recovered one. We also consider similar question for Poisson’s equation.

#### Disciplines

Science and Mathematics Education

#### Included in

Optimal Recovery of Solutions of Dirichlet Problems for Laplace's Equation

Laplace’s equation is a partial differential equation of the second order, which has a different use in mathematical physics (electrostatistics, mechanics, thermodynamics, etc.). Frequently also boundary condition is added (Dirichlet’s problem). The solution to this problem is well known. Our goal in this study is to develop an optimal method of recovery of the solution based on information we have on hand about the function (the function is not fully known. For example is known at N equally spaced points) and to compute the optimal error between the actual solution and the recovered one. We also consider similar question for Poisson’s equation.