Finite element methods for semilinear elliptic and parabolic interface problems
The authors discuss piecewise linear finite element methods for second-order elliptic and parabolic interface problems in two dimensional domains with jumps of coefficients at smooth interfaces lying on the grid. They prove optimal order convergence for the elliptic problem and extend the result to parabolic interface problems, where a semidiscrete and a fully discrete schema based on backward Euler are considered.
second-order semilinear elliptic interface problems
second-order semilinear parabolic interface problems
scientific article; zbMATH DE number 5574503
scientific article