Methods with high accuracy for finite element probability computing (Q1899979)

Two methods are proposed for finite element probability computing with high accuracy, by which the function value on one or a few nodes can be calculated without forming the total stiffness matrix. The methods use the first boundary value problem in two dimensions, i.e. the Laplace equation. One method is a probability multigrid method and the second the boundary thickening method. As an example the problem \(\Delta u = 0\) in \(\Omega\), \(u = \sin y e^z\) on \(\Omega\), \(\Omega = \{(x, y);\;0 \leq x \leq 1\), \(0 \leq y \leq 1\}\) is analyzed. The results are tabulated.