Lawyers for Apple Inc. (Nasdaq: AAPL) and Samsung Electronics Co. are scheduled today to make their final arguments to a jury following a three-week trial over patents for smartphones and tablets after top executives at the companies talked by phone and couldn’t resolve their dispute.

U.S. District Judge Lucy Koh spent Monday with attorneys negotiating the fine-print of jury instructions and a verdict form. Absent from the courtroom were the most visible lawyers throughout the trial, Charles K. Verhoeven representing Samsung, and Harold McElhinny for Apple, who are the most likely candidates to leave the nine-member jury with final impressions before the panel huddles for deliberations starting later today or tomorrow.

“These are all first-rate lawyers,” Mark Lemley, a Stanford Law School professor, said in an e-mail. “This is the time to return to the themes of the opening and explain how the testimony the jury has listened to for three weeks matters. It’s also the time to pick a damages number and a simple theory for why it is the right one.”

Apple, based in Cupertino, California, sued Samsung in April 2011, and Suwon, South Korea-based Samsung countersued.

The case is the first to go before a federal jury in a battle being waged on four continents for dominance in a smartphone market valued by Bloomberg Industries at $219.1 billion.

Apple seeks $2.5 billion to $2.75 billion in damages for its claims that Samsung infringed four design patents and three software patents in copying the iPhone and iPad. Apple also wants to make permanent a preliminary ban it won on U.S. sales of a Samsung tablet computer, and extend the ban to Samsung smartphones.

Royalties Claim

Samsung seeks as much as $421.8 million in royalties that the company claims it’s owed for Apple’s infringement of two patents covering mobile-technology standards and three utility patents.

Koh, who has at times scolded lawyers on both sides during hard-fought battles over evidence, drew a line Monday  when attorneys sought to introduce more filings to “preserve” their record for an inevitable appeal.

“You’ve preserved enough, you’ve got a petrified forest here,” she said. “Enough is enough.”

For hours, the two sides argued about the language of an “adverse inference” that would be read to jurors explaining each company’s failure to preserve documents that the opposition would later seek as evidence.

‘Reasonable Expectation’

Koh said she wasn’t convinced by Apple’s arguments that it lived up to its commitment to save and later produce records — including e-mails to and from the company’s late co-founder, Steve Jobs — at a time when it should have had a “reasonable expectation” of litigation with Samsung. A magistrate judge in July had reached a similar conclusion about about Samsung’s automated destruction of e-mail that the iPhone maker wanted to use at the trial.

The companies finally agreed that instead of jurors being told that both companies had destroyed potential evidence, they would be told nothing at all.

In today’s closings, McElhinny may remind the jury of the evidence that Apple displayed, including records of internal discussions at Samsung, to try to show that the South Korean company changed the designs of its devices to match those of the iPhone and iPad. He may also mention the paid expert witness who testified that 21 Samsung smartphones copied Apple’s patented technology for “rubberbanding,” the way an iPad or iPhone screen seems to bounce when a user scrolls to the end of a file.

Rounded Corners

For Samsung, Verhoeven may use visual exhibits to emphasize that before the iPhone was introduced in 2007, Samsung made different types of mobile phones, including some with the look and shape that Apple claims as its own — rectangular, with rounded corners.

Samsung’s lawyer may also revisit the testimony of a news technology pioneer, Roger Fidler, whose original prototype for a flat-screen tablet predated the 2010 release of the iPad by almost 30 years, and who said he actually shared his ideas with Apple in the mid-1990s.

The judge has tried repeatedly to get the companies to resolve the case out of court. At Koh’s urging, Apple Chief Executive Officer Tim Cook spoke yesterday with Samsung’s former CEO, Choi Gee Sung, marking at least the second time they’ve talked about the case, and they weren’t able to reach an agreement, a lawyer for Samsung, Kevin Johnson, told the judge at the end of the day.

For either company to win, federal rules require a unanimous jury verdict.

The case is Apple Inc. v. Samsung Electronics Co. Ltd., 11- cv-01846, U.S. District Court, Northern District of California (San Jose).