A finite element technique for solving first-order PDEs in L-P

摘要

An approximation technique for solving first-order PDEs in L-p(Omega), 1 less than or equal to p < +&INFIN;, is proposed. The method is a generalization of the least-squares method to non-Hilbertian settings. A priori and a posteriori error estimates are proven. Numerical tests in L-1(&UOmega;) show that this type of technique can handle discontinuities without resorting to limiting procedures.